I need help with the 2nd question 1. A spaceship leaves Earth traveling 0.659c.

Question

I need help with the 2nd question

1. A spaceship leaves Earth traveling 0.659c. A second spaceship leaves the first spaceship at a speed of 0.864c with respect to the first. Calculate the velocity of the second ship with respect to Earth if it is fired in the same direction the first spaceship is already moving. Express as fraction of c and take the direction of the first spaceship as the positive direction.

2. Calculate the velocity of the second ship with respect to Earth if it is fired directly backward toward Earth. Express as fraction of c and take the direction of the first spaceship as the positive direction.

Explanation / Answer

(b) form the theory of relativity

u' =[u+v] /[ 1 + (uv /c2 ) ]
when the second spaceship is fired directly backward toward Earth,
u = 0.659c
v= -0.864c
so u' = [ 0.659 c+ (-.864c) ] / [ 1 + ([.659)* (-.864 c2) /c2 ]
= [-0.205 c] / [ 1-0.5694]
u'= -0.476 c.

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