A spaceship of mass m x 1ong kg obtains its power by converting mass into energy

Question

A spaceship of mass m x 1ong kg obtains its power by converting mass into energy. a) how much mass Delta (m) must be converted into kinetic energy to accelerate the spaceship from rest to 0.6c? b) The spaceship at 0.6c is 2 light years away and approaching earth. It launches a shuttle toward earth at the speed of 0.8c in the reference frame of the spaceship. What is the speed of the shuttle measured by someone on earth? c) For someone in the shuttle, how far is earth? d) For someone in the shuttle how long will it take for the shuttle to reach the earth?

Explanation / Answer

(4) KE = (Y - 1) m1 c^2

Y = 1 / sqrt(1 - (v/c)^2) = 1/sqrt(1 - 0.6^2)

Y = 1.25

KE = 0.25 m1 c^2

KE = 0.25 m1 c^2 = m2 c^2

0.25m1 = m2

and m1 + m2 = m = 2 x 10^9 kg

m1 + 0.25m1 = 2 x 10^9

m1 = 1.6 x 10^9 kg .....mas of spaceship

Converted mass = 0.25m1 = 0.4 x 10^9 kg .......Ans

(B) v = ((0.6c) + (0.8c)) / (1 + (0.6c)(0.8c)/c^2)

v = 1.4 / 1.48

v = 0.95c

(c) for someone in spaceship,

Y = 1 / sqrt(1 - 0.95^2) = 3.20

d = 2 / Y = 0.62 light years

(d) t = 0.62 light year / 0.95c

= 0.66 years

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