A starship passes Earth at 80% of the speed of light and sends a drone ship forward at half the speed of light rela - tive to itself. Show that the drone travels at 93% of the speed of light relative to Earth.

Check Explanation

Explanation:

Let the speed of the drone relative to earth be u = ?

Let the speed of the drone relative to the starship be u' = 0.5c

Let the speed of the starship relative to earth be v = 0.8c

In the theory of relativity,

The 3 speeds are related thus

u = (u' + v) / [1 + (u'v/c²) ]

u = (0.5c + 0.8c) [1 + ((0.8c * 0.5c) / c²) ]

u = 1.3c/[1 + (0.4c²/c²) ]

u = 1.3c/1.4 = 0.9286 c = 0.93 c = 93% c