Question

A 1500 kg weather rocket accelerates upward at 10m/s2. It explodes 2.0 s after liftoff and breaks into two fragments, one twice as massive as the other. Photos reveal that the lighter fragment traveled straight up and reached a maximum height of 530 m.

What was the speed of the heavier fragment just after the explosion?

Answer 1

Speed of the rocket just before explosion is V0 = 10*2 = 20 m/s

Let the fragments be m and 2m, then m + 2m = 1500 kg => m=500 kg

By momentum conservation, we have

1500*20 = mV1 + 2mV2

Now, the lighter fragment reached 530 m, so by energy conservation, 0.5*m*V1^2 = mgh

=> V1 = sqrt(2gh) = sqrt(2*9.8*530) = 102 m/s

So, 1500*20 = 500*102 + 1000*V2 => V2 = -21 m/s, that is, 21 m/s in downward direction