A rocket ship leaves at a speed of 35c When a clock on the r

A rocket ship leaves at a speed of 3/5c. When a clock on the rocket says 1 hour has elapsed, the rocket ship sends a light signal back to earth. According to earth clocks, when was the signal sent? According to earth clocks, how long after the rocket left did the signal arrive back on earth? According to the rocket observer, how long after the rocket left did the signal arrive back on earth?

Solution

Time measured by earth deltat_E = deltat_R / sqrt [1 - 9/25]

= deltat_R / sqrt [16/25]

= 1 hr / [4/5] = 5/4 * 1 hr

= 1.25 hr

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time for the light signal to travel to earth deltat_L,E

c deltat_L,E = 3/5 c * 5/4 hr

= 3/ 4 c.hr

deltat_L,E = 3 / 4 hr

total time = 3 / 4 hr + 5/4 hr = 2 hrs

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deltat_total,R = 5 / 4 * 2 = 2.5 hr

3 / 5 c hr = (c - vR) * deltat_L,R

deltat_L,R = [3 / 5 c hr] / [c - 3/5 c] = 3/2 hr

Total time it takes the signal to reach earth = 3/2 hr + 1 hr

= 2.5 hrs