Question

In moving away from Planet Z, a spacecraft fires a probe with a speed of 0.19 c, relative to the spacecraft, back toward Z.
If the speed of the spacecraft is 0.50 c relative to Z, what is the velocity of the probe as seen by an observer on Z?
                           c,samedirectionasspacecraft

Answer 1

Let Planet Z be at rest.

Spacecraft A is moving away from Z at speed = 0.5c

A fires a probe B back towards Z at speed ( relative to itself )= 0.19c

What is speed of B as seen by Z?

Z               B          A

rest          <----          ----->

0            -0.19c     0.5c

Now

Speed of A rel to Z = v = 0.5c

Speed of B relative to A = u =?

Speed of B relative to A = u' = - 0.19c (opposite direction of motion)

Now addition of velocities in Special relativity says:

This can also be written as :

to find u'.

Substitute given values:

Thus the speed of probe B as seen by an observer on planet Z = 0.343c towards itself.