What is d speed of craft relative 2 earth if john watch 3601 sec elapse between 1 pm to 2 pm on craft's clock?

Question

craft is moving relative to earth

Answer 1

Let dt be the time elapsed in on John's clock ( 1 hour  = 3600 s) and dt' be the time elapsed on the moving clock (3601 s).  The two are related by:

dt' = dt/sqrt(1-(v/c)^2) where v=speed o moving clock and c = speed of light

SOlve for v

dt'/dt = 1/sqrt(1-(v/c)^2)  --> (dt/dt')^2 = 1 - (v/c)^2

v/c = sqrt(1- (dt/dt')^2))  --->  v = c*sqrt(1 - (dt/dt')^2) = 0.0236 c = 7.07e6 m/s

Answer 2

time dilation

t' = t/√(1-v²/c²)

3601/3600 = 1/√(1-v²/c²)

0.9997223 = √(1-v²/c²)

1-v²/c² = 0.9994447

v²/c² = 0.0005553

v² =  0.0005553 * 9 e16

v = 0.070696 e8

or 7 percent of light speed, or 7070000 m/s

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