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Walking up and down a hill 2017-09-19
From Justina:
At 2:20 p.m. Jack is at the top of the hill and starts walking down at the exact same time that Jill, who is at the bottom of the hill, starts walking up. If they maintain the uphill speed of 2mph and downhill speed of 4mph and the distance from the bottom to the top of the hill is 1.5 mi, at what time will Jack and Jill meet?
Answered by Penny Nom.
Up a hill and down again 2017-09-17
From justina:
Jack and Jill travel up a hill at a speed of 2mi/h.they travel back down the hill at a speed of 4mi/h.what is their average speed for the entire trip? express your answer as a mixed number
Answered by Penny Nom.
A car on a rough road and a concrete road 2017-08-27
From Ken:
A car is driven on a rough road at a speed of 25km and then on a concrete road with a speed of 70kph. The car has 5.5 hours to travel 225km. How long did the car travel on concrete road?
Answered by Penny Nom.
How fast am I travelling? 2017-06-24
From corey:
if i travel 2 miles in 10 seconds, how fast am i travelling please
Answered by Penny Nom.
A man drives 48km in 45 minutes 2017-06-03
From Jamal:
A man drives from Ibadan to Oyo a distance of 48km in 45 minutes. If he drives at 72km/h where the surface is good and 48km/h where the surface is bad. Find the number of kilometers of good surfaces
Answered by Penny Nom.
Initial velocity 2017-05-23
From Annelle:
a body is thrown vertically downward from a height above the ground. determine the initial velocity and the height of the starting point if after 4 secs it reaches the ground with velocity of 68 m/s.
Answered by Penny Nom.
Yards per second to miles per hour 2017-05-11
From Scott:
If a soccer ball travels 30 yards or roughly .017 miles in 2 seconds how fast was the ball going in mph?
Answered by Penny Nom.
Feet per second to miles per hour 2017-01-27
From ron:
if a vehicle travels 50 feet in 2.5 seconds what is the speed in mph. 3600 sec in hour /5280 feet in a mile i get .68181818. how do i figure the 2.5 seconds. all the calculators I've used show 34 mph is that correct or am i forgetting the 2.5 second. please help.
Answered by Penny Nom.
Angular speed 2017-01-21
From Kenzi:
A wheel of radius 14 inches is rotating 45°/sec. What is the linear speed in in/sec and the angular speed in RPM? (Round your answers to three decimal places)

I already found the linear speed. I got 10.996 in/sec. I don't know how to find the angular speed.

Answered by Penny Nom.
John and Max walk to meet each other 2016-05-29
From abhay:
The speeds of John and Max are 30 km/h and 40 km/h.Initially Max is at a place L and John is at a place M. The distance between L and M is 650 km. John started his journey 3 hours earlier than Max to meet each other. If they meet each other at a place P somewhere between L and M, then the distance between P and M is?
Answered by Penny Nom.
At what time will Sara catch up with Jake? 2016-05-07
From Laura:
At 11:00 a.m., Jake started driving along a highway at constant speed of 50 miles per hour. A quarter of an hour later, Sara started driving along the same highway in the same direction as Jake at the constant speed of 65 miles per hour. At what time will Sara catch up with Jake?
Answered by Penny Nom.
A 3 hour river cruise 2016-05-06
From Jan:
A 3 hour river cruise goes 15km upstream and then back again.The river has a current speed of 2km/h.what is the boat's speed and how long was the upstream journey?
Answered by Penny Nom.
A road trip word problem 2016-04-10
From Marc:
While on a road trip I imagined this random word problem. Suppose I start a trip of 75 miles. My initial speed is 75 miles per hour. After every mile traveled I decrease my speed by one mile per hour. After the first mile I decrease my speed to 74 miles per hour and so on for each subsequent mile traveled. How long will it take to complete the 75 mile journey?
Answered by Penny Nom.
Shooting a ball at a target 2016-02-16
From Thys:
Hi
I have a problem with the formula that i use .(for programming)
I have looked all over the web to find a solution but no luck.
I have a cannon that shoots a ball at a target
I use this formula to calculate what my initial velocity must be to hit the target at a angle of 30 degrees and a distance of 15m (the cannon and target position is known) It works perfectly if both is at same height but if one is higher or lower it miss.

In an example I am working with the range is 30m, the angle is 45 degrees and the target is 10m higher than my position.
Please help
Formula = V0 = √RG / Sin(2α)

Answered by Harley Weston.
Speed and velocity 2016-02-14
From kechi:
A boat sails south through Chesapeake Bay. It takes 10 hours to sail 110 kilometers. Describe the boat's motion. Calculate the boat's speed and velocity, showing the calculations. Explain how the boat's speed is different from its velocity
Answered by Penny Nom.
Travelling with and against he current 2016-02-09
From Lloyd:
A boat travelled 210 miles downstream and back. The trip downstream took 10hrs, the trip back took 70hrs
1. what is the speed of the current?
2. what is the speed of the boat in still water?

Answered by Penny Nom.
Average rate for a return trip 2015-03-14
From Michael:
Jeffrey drove to a town 25 miles away at an average speed of 50 miles per hour. The return trip along the same route took 20 minutes longer than the trip to town. Determine the average speed in miles per hour for Jeffrey's round trip.
Answered by Penny Nom.
Istanbul to Lagos 2015-03-03
From Victor:
A plane flies from Istanbul to Lagos at 800km/h and then returns to Istanbul at 900km/h. The return trip takes 1 hour less than the flight to Lagos. What is the distance between Istanbul and Lagos?
Answered by Penny Nom.
Speed, distance and time 2015-02-06
From Terry:
How many seconds would it take to travel 0.18 km at a speed of 130km per hour?
Answered by Penny Nom.
Two cars pass each other going in opposite directions 2015-02-03
From Caroline:
Two cars pass each other going i opposite directions. One car is going 100 km/h and the other is going 80 km/h. How far apart will the two cars be after driving 45 minutes at these rates of speed?
Answered by Penny Nom.
A train from Vancouver to Whistler 2015-02-02
From Tea:
Serena and Nina are taking a train from Vancouver to Whistler, a 160km trip. If the average speed is decreased by 16km/hr, the trip will be 1/2 hours longer. What is the average speed of the train? Thanks :)
Answered by Penny Nom.
What is the speed of the boat in still water? 2014-10-30
From Adam:
The current in a stream moves at a speed of 2 km/h. A boat travels 38 km upstream and 38 km downstream in a total time of 3 hr. What is the speed of the boat in still water?
Answered by Penny Nom.
Revolutions per minute 2014-10-24
From Edward:
Hello; I have a 28.2 inch diameter tire; do not worry about engine RPM or gear ratios, please tell me what the RPM of that tire is at 8 MPH and 64 MPH. Thank you.

Sincerely; Edward

Answered by Penny Nom.
Problem solving 2014-09-08
From hubert:
a car left the house and travelled at an average speed of 60 kph.how many minutes will it take for the car to reach the school which is 8 km away from the house
Answered by Penny Nom.
A car passing a bus 2014-08-24
From Athish:
the driver of the car is travelling at 36 km/hr and spots a bus 80 m ahead of him after 1 hr the bus is 120 m behind the car what is the speed of the bus
Answered by Penny Nom.
Distance, speed and time 2014-08-13
From abdel:
Mac walked to a park from the college at 5 km/h. 10 minutes later, Steve started riding his bike at 15 km/h to the same park to meet Mac. They arrive at the same time at the park. How far is the park from the college?
Answered by Tyler Wood.
Angular speed 2014-06-29
From andrea:
a wheel having a radius of 10cm rotates such that the linear speed at its rim is 30mls. what is the angular speed of the wheel in rpm?
Answered by Penny Nom.
A speed word problem 2014-02-24
From kiss:
Hank bicycles 5 km/h slower than Kelly. In the time that it takes Hank to bicycle 42 km, Kelly can bicycle 57 km. How fast does each bicyclist travel?
Answered by Penny Nom.
One train overtaking another 2013-11-11
From kiran:
two trains of equal length are running in parallel tracks in the same direction with the speed of 60km/hr and 90km/hr respectively the latter completely crosses the former in 30 seconds the length of each train is in mtr
Answered by Penny Nom.
Distance as a function of acceleration 2013-07-10
From Tom:
If you start at a stoplight and your acceleration is 16t - t^2, how far have you gone after 8 seconds?
Answered by Penny Nom.
Swimming upstream and downstream 2013-02-15
From Kimberly:
a beaver swims down to its lodge 4 times faster than it swims upstream. how many times faster is its speed in still water than the speed of the stream?
Answered by Penny Nom.
Angular velocity 2012-09-05
From Kyra:
A belt connects a pulley of radius 8cm to a pulley of radius 6cm. Each point on the belt is travelling at 24 cm/sec. Find the angular velocity of each pulley.
Answered by Penny Nom.
Two cars approach a right-angled intersection 2012-04-10
From Michael:
Two cars approach a right-angled intersection, one traveling south a 40km/h and the other west at 70km/h. When the faster car is 4km from the intersection and the other case if 3km from the intersection, how fast is the distance between the car cars changing?
Answered by Penny Nom.
How long will it take lee to catch up with jodie? 2012-03-21
From kirsten:
for example, if jodie is on the bus travelling at 10 m.p.h and lee is walking at 4 m.p.h how long will it take lee to catch up with jodie?? what is this mathematical name for this
Answered by Harley Weston.
Parametric equations 2 2012-02-25
From Kathy:
If the angle at time 0 is not 45 degrees how can you find the initial velocity? Ball thrown from height of 7 feet. Caught by receiver at height of 4 feet after traveling 90 feet down the field. Find initial velocity. You had a similar problem answered but the angle was 45 degrees so the cos and sin were equal and the equations were simpler to work with. Thank you!
Answered by Harley Weston.
Jack and Kate set off in their cars ... 2012-02-13
From akiri:
Jack and Kate set off in their cars from the same point to travel the same journey. Jack has a start of eight minutes before Katie sets off. If Jack travels at 50mph and Katie travels at 75mph, how many miles will be travelled when the two cars are level?
Answered by Penny Nom.
There is a police officer in pursuit of suspect 2012-02-01
From Jay:
There is a police officer in pursuit of suspect. They suspect is driving on a straight road traveling at 79 mph, the officer is 233 yds away, traveling at 92 mph, the suspects car 5 ft long and the officers car is 5.3 ft long, how long will it take to have the front of the officers car, equal to the front of the suspects car down to the tenth of a second.
Answered by Harley Weston.
Running 5 km 2012-01-12
From Fayeann:
What amount of time will it take a person running 7 m/s to travel a distance of 5 km?
Answered by Penny Nom.
The average speed for the whole journey 2011-10-30
From Shahzad:
a train travels 68 Km at an average speed of 51Km/h. It then travels another 20Km at an average speed of 40Km/h before reaching its destination. Calculate the average speed for the whole journey?
Answered by Penny Nom.
37 miles in 3 seconds 2011-10-20
From Joyce:
Jake can travel 37 miles in 3 seconds,please calculate jake's rate of speed.(round to 2 decimal places)
Answered by Penny Nom.
What is the speed of the boat in still water? 2011-10-07
From Hannah:
The speed of a stream is 3 mph. A boat travels 10 miles upstream in the same time it takes to travel 16 miles downstream. What is the speed of the boat in still water
Answered by Penny Nom.
Driving to meet Mary 2011-08-24
From Denise:
mary leaves St Paul traveling 2000 miles @ 55 MPH; John leaves LA traveling 2000 miles @ 45 MPH how many miles will John had traveled to meet mary?
Answered by Penny Nom.
Two ships 2011-04-05
From Gevork:
Ship A is sailing due south at 16 mph. At the same time, a second ship B, 32 miles south of A, is sailing due east at 12 mph.
(a) at what rate are they approaching or separating at the end of one hour?
(b) At what rate are they approaching or separating at the end of two hours?
(c) When do they cease to approach each other and how far apart are they at that instant.

Answered by Penny Nom.
Two boats 2011-03-29
From Mamie:
Two speed boats leave the port of San Francisco traveling in opposite directions at the same time.One boat travels 8 knots per hour faster than the other.After one day's travel they are 1,920 nautical miles apart.What are the speeds of the two boats.
Answered by Penny Nom.
What is its speed in miles per hour? 2011-01-06
From Miriam:
An airliner travels 125miles in 15minutes. What is its speed in miles per hour?
Answered by Penny Nom.
80 miles in 40 minutes 2010-12-08
From james:
i travel 8o miles in 40 minutes. how fast am i going in mph
Answered by Penny Nom.
Angular speed 2010-12-03
From Julie:
If the angular speed of a circle is 360 degrees divided by the time it took to rotate, how do I calculate ones that have greater rotations than the amount of time? I mean, you calculate the angular speed of a merry-go-around that spins once every 5 seconds by doing 360degrees/5 sec, but how do you calculate a merry-go-around that has 16 rotations every 4 seconds?
Answered by Penny Nom.
What is its speed in still air? 2010-11-28
From Shelby:
An Airplane flies a certain distance in 3 hours going WITH a 40km/hr wind. It travels the same distance in 5 hours when going against the wind. What is it's speed and how long would it take to travel the same distance in still air? Distance = speed x time
Answered by Penny Nom.
What are the speeds of the boats? 2010-10-21
From Adori:
Two boats leave the port of San Francisco traveling in opposite directions at the same time. One boat travels 8 knots per hour faster than the other. After one day's travel they are 1920 nautical miles apart. What are the speeds of the boats?
Answered by Penny Nom.
John and Mary are 200 miles apart 2010-10-20
From Sarah:
two people, john and mary, are 200 miles apart and leave at the same time to meet. They are driving toward each other at constant rate on the same straight road. John is traveling at 45 mph and Mary is traveling at 35 mph. When they meet, how many miles will they be from john's house?
Answered by Penny Nom.
Two cars 2010-09-30
From Amanda:
Two cars, 142 miles apart, start moving towards each other at the same time. One is moving 3 times as fast as the other. If they meet 1.7 hrs later, find the average speed of the slower car in miles per hour?
Answered by Penny Nom.
Two cars on a circular track 2010-08-12
From david:
If two cars starts to drive at point 1 and go in a circle when will they meet? (one cars speed is faster the other ) all I need is a formula
Answered by Tyler Wood.
Angular velocity 2010-03-17
From Lindsay:
Determine the angular velocity, in radians per second, of a 14-inch car wheel, if the car is traveling at 60 miles per hour
Answered by Harley Weston.
At what rate are the people moving apart? 2009-11-01
From saira:
A man starts walking north at 4 ft/s from a point P. 5 minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 minute after the woman starts walking ?
Answered by Harley Weston.
How fast am i going? 2009-09-28
From ron:
how fast am i going if i drive 40 miles in 20 minutes...what is the formula for figuring this out.
Answered by Leeanne Boehm.
Initial Velocity of a Car Plunging Off a Cliff 2009-06-07
From Mimi:
A car fails to take a sharp turn on a flat road and plunges off a cliff. The car lands 65m horizontally and 43m vertically from where it left the edge of the cliff. How fast was the car travelling?
Answered by Stephen La Rocque.
Two Boats 2009-05-16
From Simon:
Two boats, one travelling towards the east and the other travelling towards the north, are 10 km apart afetr an hour. If the speed of one boat is 2 more than the speed of the other boat, what is the speed of the faster boat?
Answered by Stephen La Rocque.
Two airplanes are 300 miles apart 2009-04-22
From afzalsultan:
Two airplanes are 300 miles apart and flying directly towards each other.One is flying at 200 miles per hour, and the other at 160 miles per hour.How long will it take for the two planes to meet
Answered by Robert Dawson.
Passing three cars 2009-04-16
From Larry:
If 3 cars are going 50 mph, and a fourth car pass the first 3 cars in 200 feet, how fast is the fourth car going?
Answered by Stephen La Rocque.
How many miles per hour was it traveling? 2009-04-04
From Regina:
a car traveled 16 miles in 30 minutes. How many miles per hour was it traveling?
Answered by Penny Nom.
The speed of a tire in revolutions per minute 2009-03-28
From Jules:
Suppose that a tire on a car has an outer diameter of 2,5 feet. How many revolutions per minute does that tire make when the car is travelling 60 miles per hour? (hint:first find the angular velocity in radians per minute.)
Answered by Harley Weston.
A 5 ounce object traveling at 60 mph 2009-03-27
From James:
if a 5 ounce object traveling at 60 mph at 100 feet above the ground, how far will it travel forward before hitting the ground.
Answered by Robert Dawson.
A dead fly is stuck to a belt that passes over two pulleys 2009-03-21
From Jules:
A dead fly is stuck to a belt that passes over two pulleys 6 inches and 8 inches in radius. Assuming no slippage,how fast is the fly moving when the large pulley (8 inches) makes 21 revolutions per second ? How many revolutions per second does the small pulley make ? How long will it take the dead fly to travel 1 mile ?
Answered by Penny Nom.
A falling object 2009-02-01
From Tamara:
We drop an object from rest (i.e. its initial spped is zero. It is falling freely toward the ground. What will be its speed after 5 seconds of falling?
Answered by Penny Nom.
What will be its speed after 10s? 2009-02-01
From Tamara:
An object has an initial speed of 5 m/s and is accelerating with 2 m/s2 (m/s squared) acceleration. What will be its speed after 10s?
Answered by Penny Nom.
A belt drives a pulley 2008-11-03
From Rebecca:
A point on a belt is moving at the rate of 30 ft/sec and the belt drives a pulley at the rate of 200 rpm. What is the radius of the pulley?
Answered by Penny Nom.
Linear and Angular Velocity 2008-10-10
From Matthew:
The pedal and gear relationship of a bicycle is shown. The radii of the gears are r(sub1) = 5 cm and r(sub2)= 12 cm. The radius of the wheel is r(sub3) = 30 cm. How many rotations per minute of the pedal gear will produce a racing cyclist's speed of 60 km per hr. For a diagram: http://bikepedalsgears.weebly.com/
Answered by Stephen La Rocque.
Angular & Linear Speed from a Sine Graph 2008-08-19
From Kim:
Kim, a student: I am given a graph with a wave. The amplitude is 5cm and the period is 4cm. I am suppose to find the angular speed. What I need to know is the formula for angular speed and how do I use these numbers to get the correct answer.
Answered by Janice Cotcher.
Time with Non-Uniform Motion 2008-07-21
From jenina:
An unmarked police car, travelling a constant 95km/h, is passed by a speeder travelling 145km/h. precisely 1.00s after the speed passes, the policeman steps on the accelerator. If the police car’s acceleration is 2.00m/sČ, how much time elapses after the police car is passed until it overtakes the speeder (assumed moving at constant speed)?
Answered by Janice Cotcher.
The current in a river 2008-06-12
From Joi:
To approximate the speed of the current of a river, a circular paddle wheel with radius 4 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 10 revolutions per minute, what is the speed of the current? Express your answer in miles per hour.
Answered by Harley Weston.
A cat is walking on the tread of a tank 2008-05-26
From Kathleen:
If a cat is walking on the tread of a tank travelling at 28kmh how fast does the cat have to walk to avoid falling under the tracks?
Answered by Janice Cotcher.
Throwing a ball on the moon 2008-05-21
From leria:
equation for motion of moon is h=2.67t^2 + vt + s equation for earth h=-16t + vt + s

Suppose you are on an outpost on the moon and Jan is back on Earth. Both people toss a ball from a height of 96 feet with an initial velocity of 16 feet per second. How much longer will your ball stay in motion on the moon than Jan's on the earth?

Math Central,

I'm having a difficult time understanding which numbers to plug into the formula.

Answered by Stephen La Rocque.
A crate is launched from an airplane 2008-05-10
From Michelle:
A crate is launched from an airplane, 75 feet above the ocean, with an initial vertical velocity of 60 feet per second. How many seconds will it take for the crate to hit the water? Round to the nearest hundredth.
Answered by Harley Weston.
At what value of t is the maximum acceleration? 2008-04-25
From Mary:
Velocity of a function (which is the first derivative of its position) is defined over the interval 0 to 12 using the following piecewise function: v(t)=-1 from 0 to 4, v(t)=x-5 from (4 to 8 and v(t)=-x+11 from (8 to 12. At what value of t is the maximum acceleration?
Answered by Stephen La Rocque.
What is the altitude of the plane? 2008-04-23
From tiana:
If a plane is taking off and its climbing at 380 feet per minute at 205 MPH, what is the altitude of the plane after it traveled 115 miles?
Answered by Penny Nom.
Two points moving on a straight line 2008-03-06
From laura:
Particle A travels at constant speed of 1.0ms-1 in straight line, passing particle B, at which time particle B beings traveling with constant acceleration of 0.2ms-2 until reaching Particle A.
What equations represent the displacement of particle A and particle B measure from the point they first pass?
How long does it take for particle B to catch up with particle A?
What is the speed of particle B when reaching particle A?
What distance have both particles traveled from where they first pass to where they meet again?
Calculate the displacement of both particle A and B at 2 second intervals between t=0s and t=12s?

Answered by Stephen La Rocque and Penny Nom.
Parametric equations 2008-03-05
From kumi:
I have made a picture of a football pass 45 degrees with 30yds and height of 7ft and 4ft. But I am just stuck there. I have stared at the worksheet for soo long. I have no idea how to solve this, and I don't even know where this is going (I don't understand how parametric equations work). Can you help me with this problem?

1.The quarterback of a football team releases a pass at a height, h, of 7ft above the playing field, and the football is caught by a reciever at a height of 4ft, 30yds directly downfield. The pass is released at an angle of 45 degrees with the horizontal with an initial velocity of vo. The parametric equations for the position of the football at time t are given, in general, by x(t)=(vo cosθ)t and y=h+(vo sinθ)t-16t^2.

a. find the initial velocity of the football when it is released
b. write the specific set of parametric equations for the path of the football
c.use a graphing calculator to graph the path of the football and approximate its maximum height
d. find the time the reciever has to position himself after the quarterback releases the football

Answered by Harley Weston.
A ball bearing is placed on an inclined plane 2008-02-15
From Leah:
A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is x. The distance (in meters) that the ball bearing rolls in t seconds is s(t) = 4.9(sin x)t^2. What is the speed of the ball bearing, and what value of x will produce the maximum speed at a particular time?
Answered by Penny Nom.
Two cars 2007-09-17
From Lanie:
Two cars enter the Florida Turnpike at Commercial Boulevard at 8:00am, each heading for Wildwood. One car's average speed is 10 miles per hour more than the other's. The faster car arrives at Wildwood at 11:00 am, 1/2 hour before the other car. What is the average speed of each car? How far did each travel?
Answered by Stephen La Rocque.
How many miles per hour was I driving 2007-09-11
From Gary:
How many miles per hour was I driving to go 37 miles in 13 minutes
Answered by Victoria West.
What angle does the tire turn in 60s? 2007-06-04
From San:
An automobile, travelling at 80km/h, is towing a trailer. The wheels of the trailer are 40cm in diameter. Through what angle does the tire turn in 60second?
Answered by Stephen La Rocque.
Angular velocity 2007-05-01
From Bruce:
a tachometer of a Ford Explorer reads 2,100 rpm at 60 mph. Find the equivalent angular velocity in degrees per minute and radians per minute
Answered by Stephen La Rocque.
What is the speed of the boat? 2007-04-22
From Sonja:
A boat on a river travels downstream between two points, 20 miles apart, in one hour. The return trip against the current takes 2 1/2 hours. What is the speed of the boat? The answer in the book says 14 mi/hr, but I don't understand how to figure it out. It must be very simple, but I'm stuck. Thank you so much for helping me out. This is a FANTASTIC website! -Sonja
Answered by Penny Nom.
The second derivative 2007-04-14
From Gerry:
In mathematical context,what do you understand by the term "Second Derivative"
Answered by Penny Nom.
When will the rocket hit the ground? 2007-04-05
From Megan:
A model rocket is launched at an upward velocity of 460feet per second off a platform that is 40 feet up from the ground. Use the formula h(t)= -16+vo+ho where vo is the initial velocity an ho is the initial height. A.) Find the maximum hight of the rocket. B.) How long does it take to reach the maximum height? C.) When will the rocket hit the ground?
Answered by Stephen La Rocque.
Boat trigonometry 2007-04-04
From Kimi:
Hi, I have been working on the attached math problem for my college trig class for over a week. Every avenue I've tried seems to lead either to a dead end, an unreasonable answer, or extremely complicated computations. I was able to calculate the speed of the boat to 3.51 mph, but cannot figure out the measure of angle beta. Once I can figure that out, I can do the rest of the problem. Thanks, Kimi
Answered by Stephen La Rocque.
Tina swims 4 miles upstream at 1 mph 2007-03-31
From Michael:
If Tina swims 4 miles upstream at 1 mph and back downstream to the same point to the same point at 4 mph, what is her average speed?
Answered by Penny Nom.
A beam on a lighthouse 2007-03-28
From Lisa:
A beam on a lighthouse 2000 metres away from the nearest point P on a straight shoreline revolves at the rate of 10 pi radians per minute. How fast is the beam of the light moving along the shoreline when it is 500 metres from P?
Answered by Stephen La Rocque.
The velocity of an aircraft 2007-03-22
From William:
Hello, I don't understand how to work this problem. Thanks in advance for your help!

A jet moving at 500.0 km/h due east moves into a region where the wind is blowing at 120.0 km/h in a direction 30.0 degrees north of east. What is the new velocity and direction of the aircraft relative to the ground?

Answered by Penny Nom.
How long does she have to get out of the way? 2007-02-23
From Sharon:
How do I solve this? The height h (in feet) of an object that is dropped from the height of s feet is given by the formula h = s - 16t^2 , where t is the time the object has been falling. A 6 foot tall woman on a sidewalk looks directly overhead and sees a window washer drop a bottle from the 6 story. How long does she have to get out of the way? Round to the nearest tenth. (A story is 12 feet.)
Answered by Penny Nom.
Acceleration 2007-02-20
From thomas:
Don't know if this service still exists. ACCELERATION CALCULATION initial vel 0km/hr final vel 24km/hr time 3s
Answered by Stephen La Rocque.
Increasing speed and decreasing time 2007-02-18
From Nigel:
I am completely lost...can you help with this: The time, t, to travel a distance, d, at a constant speed, v, can be obtained from the formula: d = vt. If the speed is increased by x, find an expression to represent the decrease in time to travel the same distance.
Answered by Stephen La Rocque.
A person jumps from the roof of a house 2007-02-13
From Jessie:
A person jumps from the roof of a house 3.9m high. When he strikes the ground below, he bends his knees so that the torso decelerates over an approximate distance of 0.70m. If the mass of his torso (excluding legs) is 42kg, find a) his velocity just before his feet strike the ground , and b) the average force exerted on his torso by his legs during deceleration.

Please provide calculations and answers for comparison.

Answered by Stephen La Rocque.
Romeo is throwing pebbles 2007-02-08
From Jessie:
Romeo is chucking pebbles gently up to Juliet's window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 4.5m below her window and 5.0m from the base of the wall. How fast are the pebbles going when they hit her window?
Answered by Stephen La Rocque.
Driving on a banked roadway 2007-02-05
From William:
A race track is shaped like an inverted cone. Race cars drive around this track in a horizontal path. If a drivers speed is 34 m/s, at what distance from the tip of the cone should he drive his car if there is no friction?

THANKS IN ADVANCE FOR ANY ASSISTANCE YOU CAN PROVIDE!

Sincerely,
William Bush

Answered by Stephen La Rocque.
A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream 2007-01-27
From Liz:
A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream. The speed of the boat in still water is 15 mi/h greater than the speed of the current. Find the speed of the current.
Answered by Stephen La Rocque.
Freefalling objects 2007-01-25
From Patricia:
How long will it take a stone dropped from atop a 1000-meter tall building to reach the ground?
Answered by Stephen La Rocque.
At what speeds were they travelling? 2007-01-16
From Maria:
Kim and Julie are joining Nicole at her parents cottage for the weekend. The cottage is 150km away from their neighbourhood. Kim can leave directly after school but Julie will be leaving after band practice, an hour and a quarter later. Kim took her time and drove slowly, averaging 20km/h slower than Julie. They both arrived at the same time.
At what speeds were they travelling?

Answered by Stephen La Rocque.
Throwing a stone downwards 2007-01-12
From Momo:
a stone is thrown vertically downward with an initial speed of 14m/s from a height of 65 m above the ground. A) how far does the stone travel in the first 2.0 s? B) what is the stone velocity just before it hits the ground?
Answered by Stephen La Rocque.
Find the distance function s(t) given the acceleration function a(t) 2006-11-16
From David:
Find the distance function s(t) of the acceleration function: a(t)= sin(0.1t)/ cos^3(0.1t)
Answered by Penny Nom.
Pulleys and belts 2006-10-31
From Lynn:

A belt has a linear speed of 32 mph. It is spinning three pulleys.
Pulley A has diameter 14 in. radius = 7 inches
Pulley B has diameter 26 in. radius = 13 inches
Pulley C has radius 3 ft. radius = 36 inches

Angular speed in Radians per min for
I got
Pulley A= .08 rads/min Pulley B= .04 rads/min Pulley C=.01 rads/min

How many cm would pulley C travel in 14 seconds?


Answered by Penny Nom.
Angular speed 2006-10-04
From Jack:
A horse on a merry-go-round is 7m from the center and travels at a speed of 10km/h. What is its angular speed?
Answered by Stephen La Rocque.
The velocity of a pendulum, part II 2006-09-07
From Erin:
We saw the question in your database about the velocity of a pendulum swinging.....It is the same exact question....but there is another question......it says....

"estimate the instantaneous rate of change of d with respect to t when t = 1.5. At this time, is the pendulum moving toward or away from the wall? Explain."

Answered by Harley Weston.
A point on a bicycle rim 2006-08-01
From Sonu:
Find the speed in m/s of a point on a bicycle rim of diameter 88cm making 200 revolutions per minute.
Answered by Penny Nom.
Flying with and against the wind 2006-07-06
From Tim:
When a plane flies with the wind, it travels 800 miles in 4 hours. Against the wind it takes 5 hours to cover the same distance. Find the rate of the plane in still air and the rate of the wind.
Answered by Stephen La Rocque.
Angular velocity 2006-03-28
From Ben:
How do you (a) express angular speed in terms of linear speed and (b) express linear speed in terms of angular speed?
Answered by Stephen La Rocque.
Orbital velocity 2006-02-15
From Lizzie:

Assume the world is a spherical planet with a diameter of 1600 KM. with a uniform density or 5200 KM.

It the moon is in a circular orbit of 630 KM. above the surface of the world,what is it's orbital velocity in metres per second?Round to the nearest WHOLE number.


Answered by Stephen La Rocque.
A locus problem 2006-02-08
From Jason:
If the distance from p(1,5) is 3/4 that of the distance of a(4,-3)? find the equation of a locus.
Answered by Penny Nom.
Find the ground speed and the planes true heading. 2006-02-05
From Jimmie:
An aircraft going from city A to city B on a bearing of S69E (degrees) is traveling at a speed of 430 mph. The wind is blowing out of the north to south at a speed of 25 mph. Find the ground speed and the planes true heading.
Answered by Penny Nom.
What initial velocity is required to double the maximum height 2006-01-14
From A photographer:
A body is thrown into the air with an initial velocity V ft./sec. What initial velocity is required to double the maximum height previously obtained?
Answered by Penny Nom.
Velocity and acceleration 2005-10-27
From Candace:
When taking the integral of the position function, you get the velocity function, and the same for velocity to acceleration. So when you do each of these, you get a function. But when you integrate on a graph, you get an area under a curve. The area is un units squared- where do the units go when you make it an equation? How can a function be an area?
Answered by Harley Weston.
Speed on a bicycle 2005-07-27
From Deborah:
We are trying to figure out how many miles per hour we rode in a bike race. If the distance was l5 miles and the time it took was was 55 minutes, what is the speed?
Answered by Penny Nom.
An aircraft is flying directly from airport A to airport B 2004-10-22
From A student:
In this question, i is a unit vector due east and j is a unit vector due north. An aircraft is flying directly from airport A to airport B, which is 2000 km from A. The velocity in still air of the aircraft is (150i+50j)km/h and the ground speed is (200i-30j)km/h. Calculate

(i) the time of flight, to the nearest min
(ii) the direction of the wind.

Answered by Penny Nom.
Cycling in the wind 2004-10-11
From A student:
A cyclist is travelling in the direction of 12i+5j at a speed of 39 km/h where i is a unit vector due east and j is a unit vector due north. The wind appears to the cyclist to be blowing with a velocity of (-4i+j) km/h. Find, correct to 1 d.p
(a) the true speed of the wind and
(b) the bearing from which the wind is blowing

Answered by Penny Nom.
Angular speed 2004-02-01
From Rachel:
A 4 inch pulley on a motor makes 1500 revolutions/minute. It is connected to an 8 inch saw blade. a. Find the angular speed of the pulley in radians/minute

b. Find the angular speed of the saw in radians/ minute

Answered by Harley Weston.
The London marathon 2004-01-27
From Nina:
After a years training, Minnie Midriffe increased her average speed in the london marathon by 25%. By what percentage did her time decrease?o
Answered by Penny Nom.
What is the speed of the automobile? 2004-01-20
From Rita:
An automobile travels toward Nashville from Cookeville. It takes 33 minutes to travel from Cookeville to Manchester, which is a 36 mile distance. If the driver continues at this pace, what is the speed of the automobile?
Answered by Penny Nom.
A rock on a string 2003-10-26
From A student:
a rock on a 4' string is rotated at 80 rpm. what is the linear speed in feet per second? in miles per hour?
Answered by Penny Nom.
A boat travels 12 km upstream... 2003-09-03
From Sohaib:
A boat travels 12 km upstream and back in 1 hour 45 minutes. If the speed of the current is 3km/hr throughout, find the speed of the boat in still water, giving your answerĘcorrect to 3 decimal places.
Answered by Penny Nom.
A helicopter rises vertically 2003-09-02
From Kate:
A helicopter rises vertically and t seconds after leaving hte ground its velocity is given in feet per second by v(t) = 8t + 40 / (t+2)2 How far above the ground will the helicopter be after 3 seconds?
Answered by Penny Nom.
A radio controled car 2003-06-08
From Robert:
I have a radio controled car (scale size 1/43). This car can travel 490 ft. per minute. I would like to know how fast that is at that scale size in miles per hour (and Kilometers per hour)?
Answered by Penny Nom.
Two rate problems 2002-09-30
From Rebecca:
  1. There are two small holes in the bottom of a tub filled with water. If opened, one hole will empty the tub in three hours; the other will empty it in six hours. If both holes are opened at the same time, how long will it take to empty the tub?

  2. An airplane flies 400 miles per hour in calm air. It can cover 900 miles flying with the wind in the same time that it can cover 700 miles against the wind. What is the speed of the wind?

Answered by Penny Nom.
A good rule of thumb when driving 2002-06-13
From Lisa:
A good rule of thumb when driving is that you should be about one car length away from the car in front of you for every 10 miles per hour that you are travelling. Suppose you follow this rule perfectly (so you are exactly the correct distance away). You are waiting at a stop light with your front bumper just touching the car in front of you. The light turns green and the car in front accelerates at a constant rate "r". Calculate how you should accelerate in order to follow the rule.
Answered by Penny Nom.
Flying with the wind 2002-05-19
From SaraJean:
It takes 6 hours for a plane to travel 720 km with a tail wind and 8 hours to make the return trip with a head wind. Find the air speed of the plane and the speed of the wind current.
Answered by Penny Nom.
A test drive 2002-04-23
From Jennie:
At 9 A.M. a test car driving at a constant speed passes a marker 50 miles from it's starting point. At noon the car is about 130 miles from the marker. If the test drive ends at 1:30 P.M., how far will the car be from its starting point?
Answered by Penny Nom.
How far does the fly fly? 2001-08-07
From Harold:
 
6 MPH                            4 MPH 
Rachel  ----------------------     Eli                        
                  10 Miles apart  

The fly is on Rachels handlebars. The fly is scared so it flys back and forth at 20 MP H. How far has the fly flown when Rachel and Eli meet?

f

Answered by Penny Nom.
A jogger 2001-03-12
From Bill:
At time t=0 a jogger is running at a velocity of 300 meters per minute. The jogger is slowing down with a negative acceleration that is directly propotional to time t. This brings the jogger to a stop in 10 minutes.

a) write an expression for the velocity of the jogger at time t.

b) what is the total distance traveled by the jogger in that 10-minute interval.


Answered by Harley Weston.
Cincinnati to Winston-Salem 2001-01-23
From Belinda:
Joan Bedney travels from Cincinnati to Winston-Salem at an average rate of 40 miles per hour and returns at an average rate of 60 miles per hour. What is her average speed for the trip?
Answered by Leeanne Boehm and Claude Tardif.
Lobbing a tennis ball 2000-10-31
From Alex:
If a tennis ball is lobbed into the air with an initial upward velocity of 12 meters per second, its velocity and height will be functions of time in flight described by the following rules:

V=12-9.8T and H=1+12T-4.9T 2

Find the maximum height of the tennis ball and the time it takes to reach that height.


Answered by Penny Nom.
Gravity 2000-09-06
From Robert Broomfield:
If they dropped a 1lb object from 40,000 feet in the air, at what speed would it it the ground?
Answered by Harley Weston.
Velocity of a pendulum 2000-08-28
From Mekca:
A pendulum hangs from the ceiling. as the pendulum swings, its distance,d cm, form one wall of the room depends on the number of seconds,t, since it was set in motion. assume that the equation for d as a function of t is: d=80+30cos3.14/3t, t>0.

estimate the instantaneous rate of change of d at t=5 by finding the average rates for t=5 to 5.1, t=5 to 5.01, and t=5 to 5.001.


Answered by Harley Weston.
PreCalculus 2000-08-09
From Angela:
Use absolute values to define the interval or pair of intervals on the real line.

 
<--|--- |--- ]--- |--- |--- |--- [---| ---|-->    
   18  19  20  21  22  23  24  25  26    

A car is moving at the rate of 50 miles per hour, and the diameter of its wheels is 2.5 feet.
a) Find the number of revolutions per minute that the wheels are rotating.
b) Find the angular speed of the wheels in radians per minute.


Answered by Harley Weston.
The speed of light 2000-06-19
From Benny Lau:
I have a personal questions. In physics,if a person is running on a train, his relative speed on the ground will be the addition of the speed of train and the person. If u have a train inside another train and inside another train, so on...... can u reach the speed of light? It would need a very long distance. But if we make all the train travel in circles. Then we don't need that much distance. So can we achieve the speed of Light?
Answered by Robert Coleman and Harley Weston.
Angular velocity 2000-05-24
From Ashley Milliman:
The crankshaft of a particular automobile engine has an angular velocity of 1,500 rpm at 30 mph. The crankshaft pulley has a diameter of 10 cm, and it's attached to an air conditioner compressor pulley with a 7 cm diameter and an alternator pulley with a 5 cm diamter

At what angular velocities do the compressor and alternator turn?

.
.
.

Answered by Harley Weston.
Running Through a Train Tunnel 2000-04-01
From Eugene Chan:
A man is running through a train tunnel. When he is 2/3 of the way through, he hears a train that is approaching the tunnel from behind him at a speed of 60 mph. Whether he runs ahead or back, he will reach an end of the tunnel at the same time the train reaches that end. At what rate, in miles per hour, is he running? (Assume he runs at a constant rate.)

I think the answer (12 mph) is wrong. Also, I believe it should read 1/3 of the way through, but don't know how to prove it. Could you come up with some way to prove it, please? I would really appreciate it.


Answered by Penny Nom.
Word problems 2000-03-31
From Amy:
Question:
  1. a north bound train left at noon. four hours later a south bound train left the same station. at 5 o'clook they were 160 miles apart. what was the rate of both if the north bound train was going 20 miles faster than the other one.
  2. clark's final exam was given 5 times the weight of the weight of a weekly test. the avgerage of 15 weekly test was 91. the overall weighted average was 85. what did he make on the final.

Answered by Penny Nom.
Travelling from A to B 2000-03-20
From Matt:
A car is traveling from point A to point B. Point A and point B are 30 miles apart. A car travels 30 miles an hour from point A to point B and then goes back to point A. How fast does the car have to go back to average 60 miles an hour?
Answered by Claude Tardif.
Rowing on the Charles River. 1997-09-17
From Fawwaz Muraisi:
On the Charles River in Boston, the Harvard bridge and the Longfellow bridge are 1 mile apart. The MIT crew starts rowing upstream at the Longfellow bridge. As the crew passes under the Harvard bridge, the coxswain's hat falls into the river. Ten minutes later, the coxswain notices and turns the boat around instantaneously. He has t he crew row back to get it, rowing at the same constant rate. By the time the team reaches the hat, they are back at the Longfellow bridge.

How fast is the river flowing?
Answered by Harley Weston.

 
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