A stationary observer sees two spaceships, A and B, moving towards him from oppo

Question

A stationary observer sees two spaceships, A and B, moving towards him from opposite directions at speeds of 0 . 8a~n d 0.9~re spectively. Calculate:

a. According to an observer on A, at what velocity is he approaching the stationary
observer?
b. According to an observer on A, at what velocity is he approaching the spaceship
B?
c. According to an observer on B, at what velocity is he approaching the stationary
observer?
d. According to an observer on B, at what velocity is he approaching the spaceship
A?

Explanation / Answer

Hi, The expression for relativistic velocity addition is                 u = (v1 - v2) / [1 - (v1*v2/c^2)] (in the final answers +ve or -ve can be used to find the directions). a) here v1 = 0.8c and v2 = 0 (observer velocity).     Hence u = 0.8c is the velocity with which observer on A is approaching stationary observer. b) here v1 = 0.8c and v2 = -0.9c (velocities in opposite direction)       Hence u = 0.988c is the velocity with which observer on A is approaching observer on B. c) here v1 = 0.9c and v2 = 0 (observer velocity)       Hence u = 0.9c is the velocity with which observer on B is approaching stationary observer. d) here v1 = 0.9c and v2 = -0.8c (velocities in opposite direction)       Hence u = -0.988c is the velocity with which observer on B is approaching observer on A. Hope this helps you. d) here v1 = 0.9c and v2 = -0.8c (velocities in opposite direction)       Hence u = -0.988c is the velocity with which observer on B is approaching observer on A. Hope this helps you. Hope this helps you.

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