Question

A special intergalactic game involves one player sending a square box of side 1m off in some direction with large rockets. The box is open in the front and back. Player to tries to get a 2 m long dart into the box. The first player wins if he can close both ends of the box on the dart or the second player misses. The second player wins if she has any part of the dart sticking out of the box when player one tries to close both ends. If the first player sends his box out of at speed 0.7c, what is the maximum speed the second player can send her dart and win?

Answer 1

This problem involves length contraction.

When objects move fast, their lengths reduce in the direction of motion.

The length l' of an object with actual length l, moving with a speed v is given by

Here, for the box, L =1 m

v = 0.7 c

So, the length of the moving box is

The length of the dart is 2m.

While moving with a velocity v, the length of the dart must be greater than 0.714 m

So,

The speed of the dart must be less than 0.9341 times the speed of light.