Question

Suppose a spaceship is approaching the Earth at half the speed of light and shoots a canister at a speed of 0.750c.

a). At what velocity will an Earth-bound observer see the canister if it is shot directly towards the Earth?

b). If it shot directly away from earth?

Answer 1

(a)

$$V=\frac{u+v}{1+\frac{uv}{c^2}}$$

$$V=\frac{0.75c+0.5c}{1+\frac{0.75c*0.5c}{c^2}}=0.91c$$

(b)

$$V=\frac{u-v}{1-\frac{uv}{c^2}}$$

$$V=\frac{0.75c-0.5c}{1-\frac{0.75c*0.5c}{c^2}}=0.4c$$