Question

How much energy is required to accelerate a spaceship with a rest mass of 110 metric tons to a speed of 0.553 c? Submit Answer Tries 0/12 Every day our Earth receives 1.550x1022 ) energy from the Sun. If we were able to use 1.05 percent of this energy to accelerate spaceships, then how many missions would be possible in one year? Submit Answer Tries 0/12

Answer 1

Part - a

The required energy is

K moch =) V1-()2-moc

by plugging all the values we get

K = (110 x 108)(3 x 108) V1 – 09.553c)2 -(110 x 10)(3 x 10%)

which gives us

K = 1.98217 x 1021 )

Part - b

Energy received by Earth is   and we use 1.05 % of this energy

1.55 x 10

therefore for one year

E = (1.55 x 10²2J)(1.05%) (365)

which gives us

E = 5.94 x 102]

hence,

the number of missions per year will be

$n = \frac{E}{K}$

by plugging the values we get

n = 5.94 x 1022 ) 1.98217 x 1021 )

which gives us

n = 29.9672

or

n = 29 full missions