Recall, from this chapter, that the factor gamma (?) governs both time dilation and length contraction, where ? When you multiply the time in a moving frame by ?, you get the longer (dilated) time in your fixed fame. When you divide the length in a moving frame by ?, you get the shorter (contracted) length in your fixed frame. A starship passes Earth at 80% of the speed of light and sends a drone ship forward at half the speed of light relative to itself. Show that the drone travels at 93% the speed of light relative to Earth.

Answer : Here Given: V = Velocity of drone with respect to Earth= 0.5 c x Vx’ Velocity of drone with respect to spaceship = 0.8 c V- Velocity of space ship with respect to earth. = 8 C- Speed of light = 3 x 10 m/s Now using the: Relativistic velocity addition formula: It can be given as below: V +x x V x V x 1+ x c2 Now substituting the values in above equation we get. V = 0.5c +0.8c x 1+ (0.5 c) . (0.8 c) c2 1.3 c x (0.4 c ) 1+ c2 1.3 c V x (1.4) = 0.928 x x 0.93 c