Many science fiction spaceships are powered by antimatter reactors. Suppose a 38

Question

Many science fiction spaceships are powered by antimatter reactors. Suppose a 38-m-long spaceship, with a mass of 15,000 kg when empty, carries 2000 kg of fuel: 1000 kg each of matter and antimatter. The matter and antimatter are slowly combined, and the energy of their total annihilation is used to propel the ship. After consuming all the fuel and reaching top speed, the spaceship flies past a space station that is stationary with respect to the planet from which the ship was launched.

What is the length of the spaceship as measured by astronauts on the space station?

Explanation / Answer

kinetic energy of space ship = energy produced by fuel

(1/2)*M*v^2 = m*c^2

(1/2)*15000*v^2 = 2000*c^2

7500*v^2 = 2000*c^2

v = c*sqrt(2000/7500)

= 0.516*c

now use length constraction equation,

L = Lo*sqrt(1 - (v/c)^2)

= 38*sqrt(1 - 0.516^2)

= 32.6 m <<<<<<<<------------------Answer

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