







A ship and a light 
20160811 

From Kirby: A ship is sailing due west when a light is observed with heading 297°50' from the ship. After the ship has travelled 2250 feet, the light heads 311°55' from the ship. If the course is continued, how close will the ship approach the light? Answered by Penny Nom. 





Travelling in a spacecraft 
20160325 

From julie: if i was travelling in a spacecraft at the speed of light and i turned on my headlight would i see the beam ? Answered by Robert Dawson. 





A 5person golf flight 
20140505 

From Jeremy: can you have a 5person golf flight and play only 3 matches so that one person plays one match each? Answered by Victoria West. 





Golf League Schedule for 15 weeks and three flights 
20140421 

From bigdog: I need help setting up a 12 team (3 flights with 3 teams in each flight) 15 week league play schedule. Each team must play teams in there perspective flight twice during the 15 week season. Answered by Victoria West. 





Find the rate at which the searchlight rotates 
20110417 

From Meredith: A searchlight is position 10 meters from a sidewalk. A person is walking along the sidewalk at a constant speed of 2 meters per second. The searchlight rotates so that it shines on the person. Find the rate at which the searchlight rotates when the person is 25 meters from the searchlight. Answered by Penny Nom. 





Trigonometry and picture hanging 
20100113 

From george: The top of a picture 1m high 0.8m from the ceiling. At a point on the ceiling directly in front of the picture, we wish to install a light so that the angle subtended by the picture equals to the angle of depression of the top of the picture. How far out from the wall should the light be installed? Answered by Penny Nom. 





e = m c^2 
20091209 

From Jim: Please explain the following formula:
E=MC2 (squared) Answered by Robert Dawson. 





Two ships and a lighthouse 
20090527 

From Chelsey: I have a question in regards to how do I know when to use tangent or cosine when determining angles. The question is: Looking north from the observation deck of a lighthouse 60 m above the sea, a lighthouse keeper sees two ships. The angles of depression to the ships is 5 degrees and 10 degrees. How far apart are the ships?
I don't understand which one to use when solving the equation. Answered by Harley Weston. 





The number of hours of daylight 
20080603 

From Marilyn: Hi, could you please help me with this question?
In a city (in the Northern Hemisphere) the minimum
number of hours of daylight is 9.6 and the maximum
number is 14.4. If the 80th day of the year (March
21) has 12 hours of daylight, determine a sine
function which gives the number of hours of
daylight for any given day of the year. (Jan 1 = 1,
Jan 2 = 2, etc).
Thank you! Answered by Harley Weston. 





Light years to miles 
20080324 

From Robert: HOW MANY MILES ARE THERE IN 7.5 BILLION LIGHT YEARS. Answered by Penny Nom. 





Related Rates (streetlamp and shadow) 
20071109 

From Casey: A street light is mounted at the top of a 15ft pole. A man 6ft tall walks away from the pole at a rate of 5ft per second. How fast is the tip of his shadow moving when he is 40ft from the pole? Answered by Stephen La Rocque and Penny Nom. 





The distance of the Andromeda Galaxy 
20071022 

From ROLY: What is 2.5 million miles x 6 trillion miles (light year)
This is the distance of the ANDROMEDA Galaxy. Answered by Stephen La Rocque. 





Probability 
20070507 

From Danielle: A box contains 3 defective lights and 5 nondefective lights. The lights are tested one at a time without replacement. What is the probability that the 3 defective bulbs will be found in the first 3 tests?
is it 1/56 by chance? Answered by Stephen La Rocque. 





What is the intensity 5m below the surface? 
20070331 

From david: I have this question which I am supposed to set it up and solve as a differential equation. I know how to solve the diffrential equation but I am having hard time understanding this question. Here is the question: The intensity of light in the ocean decreases the deeper you dive. In fact, the rate at which the intensity decreases is proportional to the current intensity. Setup the corresponding differential equation and solve for I(Y), the intensity I as a function of current intensity Y. If the light intensity 2m below the surface is 25% of the intensity at the surface, what is the intensity 5m below the surface. Can you please explain to me what does it mean by current intensity and how do I set this equation up. Thanks for the help. Answered by Penny Nom. 





A beam on a lighthouse 
20070328 

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. 





How far from Earth is Neptune? 
20060321 

From Scott: A laser beam travelling at the speed of light bounces off the planet Neptune and returns to Earth in 29 960.72 s. The speed of light is 299 792.5 km/s. How far from Earth is Neptune? Answered by Penny. 





What is 2,500 X 6 trillion miles? 
20050915 

From Roly: ANDROMEDA Galaxy is 2,500 light years away. A light year is 6 trillion miles. What is 2,500 X 6 trillion miles in a mathematical number? Answered by Penny Nom. 





A lighthouse is located on a small island,... 
20050714 

From Brittnee: A lighthouse is located on a small island, 3 km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? Answered by Penny Nom. 





Accelerating to the speed of light 
20040930 

From Lars: How long time would it take to accelerate up to the speed of light with an acceleration speed similar to 0100 seconds in 5 seconds? Answered by Penny Nom. 





A spotlight shines on a wall 
20020525 

From Barb: A spotlight on the ground shines on a wall 12m away. If a man 2m tall walks from the spotlight toward the bldg at a speed of 1.6 m/s, how fast is his shadow on the bldg decreasing when he is 4m from the bldg? Answered by Penny Nom. 





Oven lights 
20020506 

From Manny: Q.A manufacturer of stoves has to buy oven lights from from two diffrent companies because one company alone cannot meet its demand. the manufacturer purchases 60% of the oven lighs from comany A and the rest form Company B. Past experiecnce shown that 1% of Company A's oven are defective oven and 2.5% of Company B's oven light are defective. Determine the probability that a defective oven light is supplied by company A. Answered by Andrei Volodin. 





A lighthouse and related rates 
20011129 

From Melissa: A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline, and its light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? Answered by Penny Nom. 





A clap of thunder 
20011115 

From Frustrated Mom: While getting a recipe for the Thanksgiving feast. The teacher was talking on the phone with a friend who lives four miles north of her. She saw a flash of lightning through the window: fifteen seconds later, she heard a clap of thunder. Ten seconds after that she heard the thunder over the phone. Where did the lightning strike in relation to the teacher's house. (There are two possible answers. Sound travels about 1/5 mile per second. Some people say it's not good to be on the phone in a thunderstorm). Answered by Claude Tardif and Penny Nom. 





A lighthouse problem 
20011102 

From A student: A lighthouse at apoint P is 3 miles offshore from the nearest point O of a straight beach. A store is located 5 miles down the beach from O. The lighthouse keeper can row at 4 mph and walk at 3.25 mph.
a)How far doen the beach from O should the lighthouse keeper land in order to minimize the time from the lighthouse to the store?
b)What is the minimum rowing speed the makes it faster to row all the way? Answered by Harley Weston. 





Height of the lamp 
20001231 

From Joey: The figure shows a lamp located three units to the right of the yaxis and a shadow created by the elliptical region x^{2} + 4y^{2} < 5. If the point (5,0) is on the edge of the shadow, how far above the xaxis is the lamp located? Answered by Harley Weston. 





The speed of light 
20000619 

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. 

