The space bus is 2.0 km long in its own frame and moves towards planet earth at a speed of 0.6c. Jim is on the bus while Carl is on earth. Jim is sitting at the back of the bus and launches a projectile towards the front of the bus at a speed of 0.4c. Ignore any acceleration times or energy considerations. (a) How fast does Carl measure the projectile to be moving? (b) How long does Carl measure the bus in his frame? (c) How long would Carl determine it would take for the projectile to reach the front of the bus?

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Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.