The relative velocity of any two objects will never exceed the speed of light. Applying the Lorentz transformation to the velocities, equations are obtained for the relative velocities as seen by the different observers. These equations are called the Einstein velocity addition relationships.

For example:

Observer A is at rest, u = velocity of projectile as seen by A

Observer B is moving, u’ = velocity of projectile as seen by B

The projectile fired by B is u’.

If A sees B moving at velocity v, then a velocity measured by B (u’) would be seen by A as:

Answer:

u= (v+ u^')/(1+ (vu^')/c^2 )

The reserve transformation being

u^'= (u-v)/(1- uv/c^2 )

These relationships make sense at low speeds where both denominators approach 1.

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