The starship Enterprise approaches the Klingon home world with speed 0.6c relative to the planet. To announce its arrival, the Enterprise sends a message in a projectile that travels toward the planet with speed 0.4c relative to the Enterprise. At what speed does a Klingon at the surface of the planet see the projectile approach?

Question

Quizplus · Accepted Answer

To solve this problem, we can use the relativistic velocity addition formula:

v = (u + w)/(1 + uw/c^2)

where v is the relative velocity between two objects moving at velocities u and w relative to a third object, and c is the speed of light.

In this case, let u = 0.4c (the velocity of the projectile relative to the Enterprise), w = -0.6c (the velocity of the Enterprise relative to the planet), and solve for v (the velocity of the projectile relative to the Klingon on the planet).

v = (0.4c - 0.6c)/(1 - 0.4c*(-0.6c)/c^2) = 0.8c

Therefore, a Klingon at the surface of the planet sees the projectile approach with a speed of 0.8c.

The Starship Enterprise Approaches the Klingon Home World with Speed