Two rockets, A and B, approach each other as shown in the figure. A travels to the right at 0.7c while B travels to the left at 0.8c. Both speed measurements are made relative to an inertial observer.
-Determine the speed of A relative to B.

Question

Two rockets, A and B, approach each other as shown in the figure. A travels to the right at 0.7c while B travels to the left at 0.8c. Both speed measurements are made relative to an inertial observer. 
-Determine the speed of A relative to B.

Quizplus · Accepted Answer

To solve this problem, we need to use the relativistic velocity addition formula:
v = (u + v) / (1 + uv/c^2), where u and v are the velocities of A and B relative to the observer, and v is the velocity of A relative to B.

Plugging in the values given in the problem, we get:
v = (0.7c + (-0.8c)) / (1 + (0.7c)(-0.8c)/c^2) = -0.1c / (1 - 0.56) = -0.23c

The negative sign indicates that A and B are moving in opposite directions. To get the magnitude of v, we take the absolute value:
|v| = 0.23c

Therefore, the speed of A relative to B is 0.23c, which is approximately 0.96c of the speed of light. The correct answer is B.

Two Rockets, a and B, Approach Each Other as Shown