As measured from the Earth,a spacecraft is moving at speed 0.80c when it releases a probe at speed 0.60c relative to the spacecraft in a forward direction.What would be the speed of the probe as measured from the Earth?
A)0.70c
B)0.81c
C)c
D)0.95c

Question

Quizplus · Accepted Answer

From the perspective of the spacecraft, the probe is moving at 0.60c in a forward direction. However, since the spacecraft itself is already moving at 0.80c, the velocity addition formula must be used to calculate the speed of the probe as measured from the Earth:

v = (v spacecraft + v probe)/(1+ v spacecraft*v probe/c^2)

v = (0.80c + 0.60c)/(1 + 0.80c*0.60c/c^2)

v = 1.4c/1.48

v = 0.95c

Therefore, the speed of the probe as measured from the Earth would be 0.95c, which is choice D.

As Measured from the Earth,a Spacecraft Is Moving at Speed