Question

a spaceship is moving at a speed 0.5c away from an observer at rest. a boy in the spaceship shoots a proton gun with protons having a speed of 0.4c. (a) what is the speed of the protons measured by the observer at rest when the gun is shot away from the observer? (enter your answer in terms of c.) c

Answer 1

v = .5 c speed of observer relative to spaceship

V1 = -.4 c speed of protons from gun (sway from observer)

V2 = (V1 - v) / (1 - v V1 / c^2) speed of protons measured by observer

V2 = (-.4 c - (.5 c)) / (1 - (.5 c) (-.4 c ) / c^2))

V2 = -.9 c / (1 + .2) = -.75 c

One must use care in assigning signs to velocities

An observer sees the spaceship moving away at -.5 c while the protons are moving at .4 c in the positive direction