Physics rocket thrust problem?

Posted on 2014-11-21 06:09:00 in Physics by DUKE

A 2,000 kg rocket carrying 3000 kg of fuel is drifting in space when it fires its engine. While operating, the rocket engine burns 20 kg of fuel per second and the exhaust gasses leave the rocket at an exhaust velocity of ve =300 m/s relative to the rocket.

1) At some moment while the engine is firing, the rocket has mass M and is moving at velocity v, as is all the fuel it contains. After a short time ?t, the rocket has burned an amount of fuel ?m which leaves the rocket at velocity ve relative to the rocket. Write expressions for the total momentum before ?m is burned and after ?m is exhausted.

2) Set the two expressions in (1) equal and expand any products of sums and differences.

3) Delete any terms which are a product of two factors of ?m, ?v in any combination (they will be much smaller than other terms as ?t shrinks to zero).

4) Now take a limit as ?t shrinks to zero and integrate from t = 0 to t to find an expression for the velocity of the rocket as a function of time.

5) Integrate from ?m = 0 to 3000 kg (t= 0 to [3000 kg/20kg/s]). to find the change in the velocity of the rocket

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