Question

A 1000-kg space probe is motionless in space. to start moving, its main engine is fired for 5 s during which time it ejects exhaust gases at 5000 m/s. at the end of this process it is moving at 20 m/s. the approximate mass of the ejected gas is:

Answer 1

When a collision occurs, the change in momentum, is the difference in the momentums of the two objects after the collision minus the momentum of the object before the collision. From the aforementioned , we have change in momentum to be final momentum after collision - momentum before collision. But then the impulse of the fird bullet is just the change in momentum. Impulse = Ft where F = Ma. Where F= force and a is the acceleration. F = 1000* a; since a = V/t; i. e change in velocity by time. So we have 5000/5 =1000ms^2. Hence F = 1000 * 1000 = 1000000N. Then our Impulse , Ft = 1000000 * 5 = 5000000N. Momentum just before collision = 1000 * 500 = 500000. After collision we have final momentum = m * 20 where m is the mass after collsion. So we have 20M - 500000 = 5000000. 20M = 5000000-500000 = 4500000. M = 225000Kg.