This Week's Experiment - #248 Relative Speed

a car
a good driver
a long stretch of road
a cotton ball or small piece of tissue paper
a friend

OK, here is the idea. You are going to challenge someone to a throwing contest, and you are going to win. Trust me. If you do this correctly, you will win every time. Be sure that your driver knows what is going on and that everyone keeps safety in mind. You don't want to distract the driver from paying attention to the road.

Have your friend sit in the front, passenger seat. You will sit in the back seat. Wait until the car is traveling fairly fast. Now, you are going to see who can throw the cotton ball faster. You start by very gently tossing the cotton ball to your friend. Now to win, all your friend has to do is throw the cotton ball back to you and have it travel faster than it did when you threw it. Your friend will probably throw the cotton as hard as he can, which means he will lose.

If your friend threw the cotton ball much harder, why did I say that he lost? It has to do with relative speed. From the inside of the car, your friends toss seemed faster than yours, but we are looking at things from a broader perspective.

Say for example that your car is traveling at 55 miles per hour. That means that you, your friend and the cotton ball are also traveling 55 miles per hour. When you toss the cotton ball to your friend, in the same direction that the car is traveling, you add its speed to that of the car. A toss that seems to be 2 miles per hour actually adds 2 miles per hour to the speed that the cotton ball is already traveling. Someone standing by the side of the road with a radar gun would see the cotton ball with a speed of 57 miles per hour!

Now it is your friend's turn. I chose a cotton ball so air resistance would slow it down and prevent it from reaching high speeds. Lets pretend that your friend throws the cotton ball back towards you at a speed that seems to be 20 miles per hour. From your perspective, it would seem that his throw was 18 miles per hour faster than yours, but from a perspective outside the car, things are very different. Since he is throwing the cotton in the opposite direction, this time you subtract that speed from the speed of the car, not add it. That means that your friend succeeded in slowing the cotton ball down by 20 miles per hour. The person standing on the side of the road would see his throw traveling only 35 miles per hour compared to your toss of 57. An easy win. The harder he throws the cotton, the more he slows the cotton down compared to the road outside, and the larger your margin of victory. Even if he throws the cotton very gently, he must still throw it to you, which means it will be traveling in the opposite direction from the car. He still can't win.

Of course to convince your friend that you won, you will have to understand all of this well enough to explain it and have him understand it. Relative speeds can be very interesting. You can even win this challenge without a car. You just have to be sure that you are standing in the right spot. The Earth is rotating at about 1000 miles per hour. Think about where the sun rises and sets and you should be able to figure out which direction it is turning. That should let you figure out where to stand and where to have your friend stand, in order to win the challenge. Think about the turning Earth in the same way as the moving car. If you position things correctly, your throw will be adding to the speed of the Earth's rotation (letting your cotton ball reach a speed of over 1000 miles per hour!) Your friend's toss back to you will be in the opposite direction, making it slower. Just don't play this trick on an astronomer. She might add in the speed of the Earth traveling around the sun, or the speed of the sun and Earth traveling through space to work out a way to win. It all depends on your perspective.

These experiments are from Robert Krampf - The Happy Scientist

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