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

We can use the relativistic velocity addition formula to solve for the speed of ship C as measured by the captain of ship A:

v_AC = (v_AB + v_BC) / (1 + v_AB*v_BC/c^2)

where v_AB is the relative velocity of ship A as observed by ship B (0.50c), v_BC is the relative velocity of ship C as observed by ship B (0.82c), and c is the speed of light. We can plug in these values and solve:

v_AC = (0.50c + 0.82c) / (1 + 0.50c*0.82c/c^2) = 1.32c / (1 + 0.41) ≈ 0.94c

Therefore, the speed of ship C as measured by the captain of ship A is approximately 0.94c, which corresponds to choice A.

Three Spaceships A,B,and C Are in Motion as Shown in the Figure.The