







An airplane schedule 
20161014 

From Stephanie: Starting at 8:00a.m., a passenger plane leaves from an airport every 6 minutes and a cargo plane leaves every 7 minutes. When is the next time these kinds of planes will leave at the same time? Answered by Penny Nom. 





Dropping supplies from an airplane 
20130214 

From Claire: An airplane flying at an altitude of 3500 feet is dropping supplies to researchers on an island. The path of the plane is parallel to the ground at the time the supplies are released and the plane is traveling at a speed of 300 mph.
a) write the parametric equations that represent the path of the supplies
c)How long will it take for the supplies to reach the ground?
d) how far will the supplies travel horizontally before they land? Answered by Penny Nom. 





How fast is the distance between the aircraft and the car increasing? 
20121024 

From Steven: At a certain instant an aircraft flying due east at 240 miles per hour passes directly over a car traveling due southeast at 60 miles per hour on a straight, level road. If the aircraft is flying at an altitude of .5mile, how fast is the distance between the aircraft and the car increasing 36 seconds after the aircraft passes directly over the car? Answered by Penny Nom. 





A plane travelling with the wind and against the wind 
20120803 

From Gwen: The time of a plane trip of 450 miles, with the wind is 3/5 the time of the return trip against the wind. If the plane travels 120 mph in still air, what is the wind speed? Answered by Penny Nom. 





The position of an aircraft relative to the airport 
20120608 

From Dennis: "Air traffic controllers usually describe the position of an aircraft relative to the airport by altitude, horizontal distance, and bearing. Suppose an aircraft is at altitude 500m, distance 15km, and bearing 35 degrees east of north. What are the x,y, and z components (in meters) of the position vector. The xaxis is east, the yaxis is north and the zaxis is vertical. Answered by Penny Nom. 





What is its speed in still air? 
20101128 

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. 





Two jets leave denver at 9 am. 
20101015 

From Carl: two jets leave denver at 9 am. One flying east at a speed of 50 km per hour greater than the other which is traveling west. At 11 am the planes are 2500 km apart. Find their speeds. Answered by Stephen La Rocque. 





An aeroplane flying in a wind 
20090602 

From Maria: The aeroplane flies in a wind of speed 50 kph from the direction S80◦W. However, the direction in which it is pointed, and its speed in still air,
are such that its resultant speed and direction are 800 kph, and direction N71.6◦E
I need to find the size of the angle between v and vw, in degrees to one
decimal place, and find the speed at which the aeroplane would fly if the air were
still, to the nearest kph.
It would help me greatly if I could see a diagram illustrating the velocity va that the aeroplane
would have if the air were still, the velocity vw of the wind, and
the resultant velocity v of the aeroplane (diagram should be
in the form of a triangle illustrating how one velocity vector is the
sum of the other two)
Thanks Answered by Harley Weston. 





Related rates 
20090309 

From Megan: A plane flying with a constant speed of 330 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later? Answered by Harley Weston. 





How fast is the visible surface of the earth decreasing? 
20090124 

From Ray: A dive bomber loss altitude at a rate of 400 mph. How fast is the visible surface of the earth decreasing when the bomber is one mile high? Answered by Harley Weston. 





How far is the airplane from the control tower? 
20090117 

From Murtaza: An aircraft is vertically above a point which is 10 km west and 15 km north of a control tower. The aircraft is 4000 m above the ground, how far is it from the control tower? Answered by Penny Nom. 





How fast is the distance between the airplanes decreasing? 
20081110 

From Crystal: At a certain instant, airplane A is flying a level course at 500 mph. At the same time, airplane B is straight above airplane A and flying at the rate of 700 mph. On a course that intercepts A's course at a point C that is 4 miles from B and 2 miles from A. At the instant in question, how fast is the distance between the airplanes decreasing? Answered by Harley Weston. 





The flight of an airplane 
20080829 

From kobina: You are traveling on an airplane that is moving at 500 mph in a direction 40deg north of west.Therefore , You are travelling (due to the plane ) at how many mph toward the west. Answered by Stephen La Rocque. 





A package of supplies is dropped from a plane 
20080229 

From beth: An airplane flies west at a speed of 200m/s. A package of supplies is dropped from the plane to some campers. if the plane is at an altitude of 1000meters, how far from the campers should the package be dropped to land near them? ignore wind resistance. Answered by Stephen La Rocque. 





What is the speed of the plane in still air? 
20080105 

From oscar: A plane flies 400 miles with the wind and 340 miles against the wind
in the same length of time. If the speed of the wind is 24mph, what is
the speed of the plane in still air? Answered by Penny Nom. 





The velocity of an aircraft 
20070322 

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. 





Flying with and against the wind 
20060706 

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. 





Find the ground speed and the planes true heading. 
20060205 

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. 





How many passengers boarded the plane in Phoenix? 
20051103 

From Vish: Passengers boarded a plane in Phoenix. In Dallas 1/2 of the passengers got off and 4/5 of the original number got on. In Memphis 3/4 of the passengers got off and twice the number of remaining passengers got on. In Chicago 2/3 of the passengers got off the plane leaving 39 passengers. How many passengers originally boarded the plane in Phoenix? Answered by Penny Nom. 





An aircraft is flying directly from airport A to airport B 
20041022 

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 (200i30j)km/h. Calculate
(i) the time of flight, to the nearest min
(ii) the direction of the wind. Answered by Penny Nom. 





Two trig problems 
20030610 

From Bett:
I have this ongoing trouble with trig and solving triangles with laws of cosines and sines!! For example if it asks to solve triangle FGH, given angle G=102.7 , side f=14.2, and h=18.6. Now do I use law of cosines because I don't have the measure of an angle and length of the opposite side??I don't know where to go from here,I am totally confused!!! I also have a problem with this word problem I have been doing. It asks: An airplane flies 847.5 km at a bearing of 237.3 degrees. How far south and west fo its original position is it? Huh? Please help! Answered by Penny Nom. 





Two airplanes leave Dallas 
20030206 

From A student: TWO AIRPLANES LEAVE DALLAS AT THE SAME TIME AND FLY IN OPPOSITE DIRECTIONS. ONE AIRPLANE TRAVELS 80 MILES PER HOUR FASTER THAN THE OTHER. AFTER THREE HOURS, THEY ARE 2940 MILES APART. WHAT IS THE RATE OF EACH AIRPLANE? Answered by Penny Nom. 





Two rate problems 
20020930 

From Rebecca:
 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?
 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. 





An airplane problem 
19990308 

From B.M.R.: A plane left New York and headed East to its destination 3600 miles away across the Atlantic. On the way back its speed was boosted by a 50 mph tail wind and it arrived an hour early. What was its normal speed? Answered by Jack LeSage. 

