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. Pretend that the starship in the problem 1 is somehow traveling at ?c with respect to Earth and it fires a drone forward at speed ?c with respect to itself. Use the equation for the relativistic addition of velocities to show that the speed of the drone with respect to Earth is still ?c. 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.

Solution Step 1 of 2 To calculate the speed of the drone relative to earth As here the speed of starship and drone relative to earth is very high(comparable to speed of light), we have to solve this in the relativistic limit. This can be calculated using Einstein's velocity addition theorem, The speed of the object relative to rest observer is, v+u1 u = vu1 ……………….1 1+ c2 Where c is the speed of light.