While astronauts in a spaceship with a speed of 0.6c relative to Earth move outward from Earth toward Jupiter,they observe a cosmic ray shower that contains protons moving toward them.On Earth the speed of these protons is measured as 0.2c toward the spaceship.They measure the speed of the protons to be
A)0.80c
B)0.71c
C)0.95c
D)0.69c
E)0.45c

Question

Quizplus · Accepted Answer

To find the speed of the protons as measured by the astronauts, we use the relativistic velocity addition formula: $v' = \frac{v + u}{1 + \frac{vu}{c^2}}$, where $v'$ is the velocity of the protons relative to the spaceship, $v = 0.2c$ is the velocity of the protons relative to Earth, $u = 0.6c$ is the velocity of the spaceship relative to Earth, and $c$ is the speed of light. Plugging in the values, we get $v' = \frac{0.2c + 0.6c}{1 + \frac{0.2c \cdot 0.6c}{c^2}} = \frac{0.8c}{1 + 0.12} = \frac{0.8c}{1.12} = 0.714c$, which rounds to $0.71c$, making option B correct.

While Astronauts in a Spaceship with a Speed of 0