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Asteroid attack

A spacecraft is moving with a constant speed of 20,000 km/hr in outer space, which may be assumed to be an absolute vacuum, and away from any gravitational field. The mass of the spacecraft is 5,000 kg. In order to avoid collision with a cluster of asteroids, a small rocket engine, contained in the spacecraft, is turned on by remote control. The rocket produces a gas which exits into space in the direction opposite to the direction of motion of the spacecraft. The exhaust gas has a constant velocity (relative to the spacecraft) of 600 m/s and a density of 1.76 kg/m3. The rocket exit has a diameter of 100 mm. The rocket operated for 120 s and then it ran out of fuel and stopped.
a) Determine the final speed of the spacecraft.
b) In order to avoid collision, the spacecraft needs to be 5.0 km further away in its direction of motion, compared to the case in which the rocket would not be fired. Would the rocket succeed or fail in its mission to save the spacecraft?

Contributed by Stavros Tavoularis, Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada. Image from Galaxy Picture Library.

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