Question

Problem 14.50 According to an observer at rest in the Earth reference frame, ship A is moving toward ship B at speed 0.862 c0 while ship B is moving toward ship A at 0.697 c0 .Ship A sends out a shuttle module M that travels to ship B at speed 0.575 c0 relative to A. Part A When a pilot of the module sees 1.00 s pass on her clock, how much time would she observe passing on a distant clock in ship A? Part B When a pilot of the module sees 1.00 s pass on her clock, how much time would she observe passing on a distant clock in ship B?

Answer 1

(a)

For the speed of the module as measured from ship A: v = 0.575c, time dilation will occur and the time the person onboard the module will observe on a clock in ship A will be:

t = to/sqrt(1 - v²/c²)

t = 1 / sqrt(1 -(0.575c)²/c²)

t = 1.2223 s

(b)

Speed of B as measured by the module will be:

v' = (0.96078 + 0.575)c / ( 1+ (0.96078*0.575c² ) / c² )

v' = 0.98926 c

so, the observed time for ship B as measured by the module will be:

t' = 1/sqrt(1 - (0.98926c)² / c²)

t' = 6.8425 c