A spaceship with a rest length of 1500m is moving in the +x direction of 0.9c wi

Question

A spaceship with a rest length of 1500m is moving in the +x direction of 0.9c with respect to an observer on the ground. An astronaut standing at the back of the spaceship fires a bullet toward the front of the spaceship at a velocity of 0.8c relative to the spaceship.

a) What is the length of the spaceship as measured in the frame of the ground-based observer?

b) How long does it take the bullet to reach the front of the spaceship:

i. As measured in the frame of the spaceship?

ii. As measured in the frame of the ground-based observer?

iii. As measured in the frame of the bullet?

Explanation / Answer

a) Lenght remains same in any frame.

b) i. In spaceship frame,

time = 1500/0.8c = 625 * 10^-8 sec

ii . Ground-based observer,

time = 1500/(0.8c +0.9 c) = 294.11 * 10^-8 sec

iii. Frame of bullet,

time = 1500/0.8c = 625 * 10^-8 sec

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