How much energy is required to accelerate a spaceship with a rest mass of 134 me

Question

How much energy is required to accelerate a spaceship with a rest mass of 134 metric tons to a speed of 0.490 c?

Every day our Earth receives 1.55×1022 J energy from the Sun. If we were able to use 0.85 percent of this energy to accelerate spaceships, then how many missions would be possible in one year?

Hints:
In the acceleration process the energy we have is converted to the kinetic energy of the spaceship. The classical kinetic energy of an object is half of the mass multiplied by the square of the velocity. What is the relativistic form of the kinetic energy?

Explanation / Answer

here,

a)

Work = K

K = [1/SQRT(1-beta^2)-1]*mc^2

K = (1/sqrt(1 - 0.49^2)) * 134000 * ( 3 * 10^8)^2

K = 1.38 * 10^22 J

b)

1.55 * 10^22 * 0.0085 * 365 = 4.81 * 10^22 J

number of mission possible in year , n = 4.81 * 10^22 / 1.38 * 10^22

n = 3.49 but answer 4

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