Question

A spaceship travels with the speed of 0.712c relative to the earth A probe launched
from the spaceship travels at 0.823c with respect to the spaceship. What is the speed
of the probe with respect to the spaceship if it is fired (a) in the direction of travel of
the spaceship? (b) in the opposite direction?

Answer 1

Given:

the speed of spaceship = 0.712c

the speed of probe wrt spaceship = 0.823c

To Find:

the speed of probe when it is fired (a) in the direction of travel of  the spaceship =?

Explanation:

Now, we know that according to the diagram shown below, the relative speed of the probe can  be calculated as

V(probe) = the speed of probe wrt spaceship - the speed of the spaceship

               = 0.823 - 0.712

               = 0.111 c

Similarly, we can calculate for in the opposite direction as

V(probe) = the speed of probe wrt spaceship + the speed of the spaceship

               = 0.823 + 0.712

               = 1.535 c