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 0.82c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.50c. What is the speed of ship C as measured by the captain of ship A?
A) 0.94c
B) 0.23c
C) 2.2c
D) 0.54c
E) 1.3c

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 0.82c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.50c. What is the speed of ship C as measured by the captain of ship A? 
A) 0.94c 
B) 0.23c 
C) 2.2c 
D) 0.54c 
E) 1.3c

Quizplus · Accepted Answer

According to the relative velocity addition formula,
vAC = (vAB + vBC)/(1 + vABvBC/c^2)
where vAC is the relative velocity of ship C as measured by ship A,
vAB = -0.5c (negative because ship A is moving in the opposite direction),
vBC = 0.82c (positive because ship C is approaching ship B),
and c is the speed of light.
Plugging in the values,
vAC = (-0.5c + 0.82c)/(1 - 0.5c*0.82c/c^2) = 0.94c
Therefore, the speed of ship C as measured by the captain of ship A is 0.94c.

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