A physics question, Please answer ASAP

Question

A plane with a speed of 0.9c relative to the ground fires a shell in its direction. According to a system attached to the pilot, the shell appears to be moving away from it at a speed of 0.7c . What is the rate of distancing of the shell from the plane, from a system attached to the ground?

Answer 1

Let the ground be K and the plane be K'. The K' system

is moving at u=.9c WRT K. The shell is moving at v'=.7c

WRT the system K'. You want v, the velocity of the shell WRT the ground.

 

Use the velocity transformation eq: v=(v'+u)/(1+uv'/c²)

v=(.7c+.9c)/[1+.9(.7)]= 1.6c/1.63=.98c

So K would see .98c-.9c=.08c for the shell WRT K'.