Two rockets are each 1000m long in their rest frames. Rocket A, traveling at 0.800c relative to the earth, is overtaking Rocket B, which is moving in the same direction at 0.600c.
(i) According to the crew on B, how long does A take to completely pass? I.e. how long is it from the instant the nose of A is at the tail of B until the tail of A is at the nose of B?
(ii) Would the crew of A measure the same time interval according to their clocks? If so, explain why. If not, what is the time interval measured by the crew of A?
l = l0/γ --- Eqn 1
v = (v' + u)/(1 + uv'/c2) --- Eqn 2
The Attempt at a Solution
(i) Using Eqn 2, A is moving 0.384c relative to B.
Using Eqn 1, length contracted A from B's perspective = 0.923l0
From B's perspective, B is stationary, and A is moving past at 0.384c.
Time taken = (1+0.923)l0/0.384c = 1.67 * 10-5 s
Is this correct?
(ii) I am not sure, but I think the crew would measure the same time interval because of symmetry...??