Question

A spaceship A (at rest in inertial frame A) of proper length L₀=50.0m is moving in the +x direction at a speed v=0.750c as measured in the Earth frame. Another spaceship B (at rest in inertial frame B) is moving on a parallel path in the opposite direction ( -x ) with u_x=-0.600c as measured in the Earth frame. The two spaceships pass each other.

a. What is the velocity and speed parameter of spaceship B in inertial frame A, u'_x, ß' ?

b. In inertial frame A, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A?

c. In inertial frame B, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A?

d. In the Earth frame, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A?

Answer 1

A) velocity of spaceship B w.r.t A is given by velocity addition law,

Now putting values

So,

And

So,

B) time elapsed is calculated by

Where L is the contracted length as seen in inertial frame A

Which we can calculate as

So putting values we get

C)now in inertial frame B time elapsed must be dilated w.r.t frame A,

So,

So, putting values,we get

D) in earth reference frame their relative velocity is still given by u' but contracted length is w.r.t to earth for which spaceship. A is moving with v= .75c

So,

So putting values we get,