Three spaceships A, B, and C are in motion, as shown in the figure. The commander on ship B observes ship C approaching with a relative velocity of 0.78c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.31c. What is the velocity of ship C, relative to an observer on ship A?
A) 0.88c
B) 0.38c
C) 1.4c
D) 0.62c
E) 1.1c

Question

Three spaceships A, B, and C are in motion, as shown in the figure. The commander on ship B observes ship C approaching with a relative velocity of 0.78c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.31c. What is the velocity of ship C, relative to an observer on ship A? 
A) 0.88c 
B) 0.38c 
C) 1.4c 
D) 0.62c 
E) 1.1c

Quizplus · Accepted Answer

We can use the velocity addition formula to solve this problem:
v_{AC}=\frac{v_{BC}+v_{BA}}{1+\frac{v_{BC}v_{BA}}{c^2}}
where v_{XY} is the velocity of ship Y relative to ship X.

Plugging in the given values, we get:
v_{AC}=\frac{0.78c+0.31c}{1+\frac{(0.78c)(0.31c)}{c^2}}=\frac{1.09c}{1+0.2418}=0.88c

Therefore, the velocity of ship C, relative to an observer on ship A, is 0.88c.

Three Spaceships A, B, and C Are in Motion, as Shown