300 Problems In Special And General Relativity With Complete Solutions Pdf Today

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Problem 47: Two rockets move away from Earth in opposite directions. Rocket A moves at ( 0.6c ) relative to Earth, and Rocket B moves at ( 0.8c ) relative to Earth. What is the speed of Rocket A as measured from Rocket B?

Solution excerpt:
Using the relativistic velocity addition formula with Earth as the middle frame, we set ( u' = 0.6c ) and ( v = -0.8c ) (since B’s frame moves opposite to A’s direction in Earth’s frame).
[ u = \fracu' + v1 + \fracu'vc^2 = \frac0.6c - 0.8c1 - 0.48 = \frac-0.2c0.52 \approx -0.3846c ]
The negative sign indicates motion opposite to B’s direction; speed = ( 0.3846c ). The full solution discusses the physical interpretation and common sign errors.