Spaceships of the future may be powered by ion-propulsion engines in which ions

Question

Spaceships of the future may be powered by ion-propulsion engines in which ions are ejected from the back of the ship to drive it forward. In one such engine the ions are to be ejected with a speed of 0.80c relative to the spaceship. The spaceship is traveling away from the earth at a speed of 0.72c relative to the earth. What is the velocity of the ions relative to the earth? Assume that the direction in which the spaceship is traveling is the positive direction, and be sure to assign the correct plus or minus signs to the velocities.

Explanation / Answer

V of ions with respect to space ship = V ions with respect to ground + V GS / ( 1+ Vig Vgs/c^2)

0.80 C = V IG - 0.72 C/ ( 1+ Vig x -0.72 / c^2)

0.80 C ( 1+ Vig x -0.72 ) = Vig - 0.72 C

0.80 C - Vig 0.576 C = Vig - 0.72 C

1.52 C = Vig 1.576

Vig = 0..964 C

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