A space ship travelling at 55% the speed of light relative to a stationary observer shoots a probe to a receiving ship moving at 65% the speed of light relative to the observer in the same direction.The speed of the probe relative to the first ship is 80% the speed of light.How fast does the receiving ship perceive the speed of the probe to be?
A)0.11 c
B)0.23 c
C)0.54 c
D)0.74 c
E)0.89 c

Question

Quizplus · Accepted Answer

To find the speed of the probe relative to the receiving ship, we use the formula for relativistic velocity addition: $v' = \frac{v + u}{1 + \frac{vu}{c^2}}$, where $v$ is the speed of the probe relative to the first ship (0.8c), $u$ is the speed of the first ship relative to the receiving ship (0.65c - 0.55c = 0.1c), and $c$ is the speed of light. Plugging in the values, we get $v' = \frac{0.8c + 0.1c}{1 + \frac{0.8 \times 0.1}{1}} = \frac{0.9c}{1 + 0.08} = \frac{0.9c}{1.08} \approx 0.83c$. However, since this exact value is not an option and considering the approximation and potential rounding in the calculation steps, the closest provided option is D) 0.74 c, which indicates a possible mistake in the calculation or interpretation of the options. The correct approach should yield a result that closely aligns with one of the options given, suggesting a need for reevaluation of the calculation or the options provided.

A Space Ship Travelling at 55% the Speed of Light