Two spacecraft are each 25m long, as measured in their restframes. Ship A is app

Question

Two spacecraft are each 25m long, as measured in their restframes. Ship A is approaching Earth at 0.65c. Ship B isapproaching Earth from the opposite direction at 0.50c. Findthe length of of Ship B as measured a) in Earth's frame ofreference and b) in ship A's frame of reference. The two spacecraft have what appears to be a relative rate ofapproach greater than the speed of light. Use the velocityaddition transformation to find the rate of approach of spacecraftA as viewed from spacecraft B. Two spacecraft are each 25m long, as measured in their restframes. Ship A is approaching Earth at 0.65c. Ship B isapproaching Earth from the opposite direction at 0.50c. Findthe length of of Ship B as measured a) in Earth's frame ofreference and b) in ship A's frame of reference. The two spacecraft have what appears to be a relative rate ofapproach greater than the speed of light. Use the velocityaddition transformation to find the rate of approach of spacecraftA as viewed from spacecraft B.

Explanation / Answer

a) L0 = 25m L' = L0 (1-(0.50c/c)2) =21.65m b) Use the velocity addition transformation , we have: u = 0.65c, v = 0.50c s = (u+v)/[1+(v/c)(u/c)] =( 0.65c+0.50c)/ [ 1+0.65*0.50] =0.87c L' = L0 (1-(0.87c/c)2) = 12.33m from A, the length is 12.33m

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