A rocket is out in space, far away from any planet. At a certain time, it has a

Question

A rocket is out in space, far away from any planet. At a certain time, it has a mass of 2.8 x 105 kg, most of which is fuel. The engine is turn on for 160 s while fuel is consumed at a constant rate of 450 kg/s, then the engine is turned off again. The speed of exhaust from the engine relative to the rocket is 5.00 km/s. What is the rocket's thrust force?

After the engine is turned off, what is the new mass of the rocket?

How much faster is the rocket going after the engine is turned off compared to before the engine is turned on?

Explanation / Answer

Thrust force is given as V (relative)*dm/dt = 5000*450 = 2250KN

New mass of rocket = 2.8x10^5 - (450*160) = 2.08x10^5 kg

We have change in velocity = V(relative) * ln(initial mass/final mass) = 5000*ln(2.8/2.08) = 1486.25 m/s = 1.486 km/s

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