An astronaut wishes to visit the Andromeda galaxy, making a one-way trip that wi

Question

An astronaut wishes to visit the Andromeda galaxy, making a one-way trip that will take 30.0 years in the spaceship's frame of reference. Assume the galaxy is 2.00 million light-years away and his speed is constant. A) How fast must he travel relative to Earth? B) What will be the kinetic energy of his spacecraft, which has mass of 1.00 times 10^6 kg? C) What is the cost of this energy if it is purchased at a typical consumer price for electric energy, 13.0 cents per KWh? D) Suppose the astronaut's daughter, born during the trip, after hearing so much about Earth, wishes to go to Earth. It takes 30.0 years for the return journey. What will her closest relative be? Presume that each generation is 15 years, and a lifetime is 90 years. Also, the following approximation may be useful: 1/Squareroot 1 + x almostequalto 1 - x/2 for x

Explanation / Answer

t = 30 years ; d = 2 x 10^6 LY

A)we know that,

v = d/T

T = t/sqrt(1 - v^2/c^2)

v = d/t/sqrt(1 - v^2/c^2)

v = 2 x 10^6 years x c x sqrt (v^2/c^2)/30 years

after solving, v = 0.999 c

Hence, v = 0.999c

b)KE = sqrt (1 + 1/x) - 1) m c^2

KE = sqrt (1 + 1/2 x 10^-10 1 -) 1.0 x 10^6 x (3 x 10^8)^2

KE = 6.8 x 10^27 J

Cost = 6.8 x 10^27 x 1KWH/3.6 x 10^6 J x 0.13 $/KWH

cost = 2.5 x 10^20 $

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