# hw sol 9 - t t = 29 29 s s c c t c v t 92 4156 3600 5 1 1 1...

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Solutions to Homework 9 1) Use the relativistic velocity addition rule, + + = 2 2 1 2 1 1 c v v v v V where v 1 is the velocity of object 1 and v 2 is the velocity of object 2 relative to object 1. Then, the speed of the drone (relative to the Earth) would be ( 29 ( 29 c c c c c c V 93 . 0 5 . 0 8 . 0 1 5 . 0 8 . 0 2 = + + = 2) Using the formula for time dilation, 0 t t γ = and your knowledge of γ and the proper time, t 0 , you can find the time interval of the catnap in the stationary frame, ( 29 ( 29 s s c c t c v t 64 . 2126 300 99 . 0 1 1 1 1 2 2 0 2 2 = - = - = or, about 35 ½ minutes. 3) Again, use the time dilation formula to determine the time elapsed on Earth:

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Unformatted text preview: t t = ( 29 ( 29 s s c c t c v t 92 . 4156 3600 5 . 1 1 1 1 2 2 2 2 =-=-= or, about 1.15 hours. At a rate of 10 stellars per hour, the new pay would be 11.5 stellars. 4) If one kilogram of Uranium is used as fuel, only one gram of mass will be converted into energy. Using the famous equation, e=mc 2 , we’ll get: E = mc 2 = (0.001 kg)(3.0 x 10 8 m/s) 2 = 9 x10 13 joules. At a rate of 3 cents per megajoule (10 6 joules), that is 2.7 million dollars worth of energy!...
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hw sol 9 - t t = 29 29 s s c c t c v t 92 4156 3600 5 1 1 1...

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