# 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? b) If B fires the projectile backward, what is the...

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?

b) If B fires the projectile backward, what is the speed of the projectile as seen

by A?

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The speed of light (c) is considered to be the upper limit of velocity through time-space and is considered to be constant. It's also considered to be independent of the motion of the observer. If a traveler is moving at half the speed of light (0.5c) and fires a projectile forward at 0.8c, an observer at rest does not see the projectile moving at 1.3c but rather at c. Both the observer and shooter see the projectile moving at the speed of light, regardless whether it's shot forward or backward.

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

The formula for adding relativistic speeds is (w+u)/(1+w*u/c^2), where w and u are the two speeds you want to add. So, an observer at rest would see the speed of the projectile as 0.928c.

The observer B himself is moving in a velocity 0f 0.5c per unit of time. The relative forward velocity of the of the projectile with respect B is 0.8c. The realative velocity of the projectile with respect another observer at rest = sum of the speed of the observer B and the relative speed of the projectile by observer B

= 0.5c+0.8c=1.3c

b)

If B fires the projectile backward with relative velocity 0.8c, then the relative velocity of the projectile for the person at rest is still the algebraic sum of the relative velocity of the projectile to the observer B + velocity of the observer B = -0.8c+0.5C = -0..3c.