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

In order to find the velocity of ship C relative to an observer on ship A, we need to use the relative velocity addition formula:

vAC = (vAB + vBC)/(1 + vABvBC/c^2)

where vAB is the relative velocity of ship A with respect to ship B (0.31c), vBC is the relative velocity of ship B with respect to ship C (0.78c), and c is the speed of light.

Plugging in the values, we get:

vAC = (0.31c + 0.78c)/(1 + (0.31c)(0.78c)/c^2)
vAC = (1.09c)/(1+0.24)
vAC = 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 in the Figure.The