Is that going faster than light?

Classical Mechanics Level 3

Imagine a motorcycle rider moving with a speed of 0.800 c 0.800c past a stationary observer. If the rider tosses a ball in the forward direction with a speed of 0.700 c 0.700c with respect to himself, what is the speed of the ball as seen by the stationary observer?

Note: c c is velocity of light in vacuum.

1.5 c 1.5c c c 0.8823 c 0.8823c 0.9615 c 0.9615c

Farhabi Mojib by Farhabi Mojib , 23, Bangladesh

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1 solution

The formula for the addition of velocities in Special Relativity is

w = u + v 1 + u v c 2 w = \dfrac{u + v}{1 + \dfrac{uv}{c^{2}}} ,

where the relative velocities are u , v , u,v, and where c c is the speed of light. In this case u = 0.800 c u = 0.800c and v = 0.700 c v = 0.700c , so the speed of the ball relative to a stationary observer will be

w = 0.800 c + 0.700 c 1 + 0.88 c × 0.700 c c 2 = 1.500 c 1 + 0.560 = 0.9615 c w = \dfrac{0.800c + 0.700c}{1 + \dfrac{0.88c \times 0.700c}{c^{2}}} = \dfrac{1.500c}{1 + 0.560} = \boxed{0.9615c} to 4 decimal places.

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