An observer B, moving at speed 0.5c, fires a projectile forward at speed 0.8c.a) What is the speed of the projectile as seen by a rest observer A?...

The symbol c is generally used for the speed of sound. But I assume that that is not the case in this question.

Answer a)

As B is moving at the speed of 0.5, and he fires the projectile in the direction of his movement, the net speed of the projectile with respect to a stationary observer will be the sum of the speed of B and speed of projectile.

Therefore as seen by A, the speed of the projectile = 0.5c + 0.8c = 1.3c

Answer b)

As B is moving at the speed of 0.5, and he fires the projectile in the backward direction, the net speed of the projectile with respect to a stationary observer will be the speed of projectile less the speed of B.

Therefore as seen by A, the speed of the projectile = 0.8c - 0.5c = 0.3c