A two-stage rocket moves in space at a constant velocity of 5000 m/s. The two st

Question

A two-stage rocket moves in space at a constant velocity of 5000 m/s. The two stages are then separated by a small explosive charge placed between them. Immediately after the explosion the velocity of the 1150-kg upper stage is 5780 m/s in the same direction as before the explosion. What is the velocity (magnitude and direction) of the 2500-kg lower stage after the explosion?

The lead female character in the movie Diamonds Are Forever is standing at the edge of an offshore oil rig. As she fires a gun, she is driven back over the edge and into the sea. Suppose the mass of a bullet is 0.015 kg, and its velocity is +724 m/s. Her mass (including the gun) is 48 kg.

Explanation / Answer

1) M= m1+m2, m1 =1150 kg , m2 =2500 kg , v1 =5780 m/s, u =5000 m/s

from conservation of momentum

Mu = m1v1 +m2v2

(1150+2500)*5000 = (1150*5780) + (2500*v2)

v2 = 4641.2 m/s

2) (a) m1 =0.015 kg , m1+m2 = M =48 kg , u1 =724 m/s , u2 =0

from conservation of momentum

m1u1 +m2u2 = (m1+m2)v

(0.015*724) +0 = (48)v

v= 0.226 m/s

(b) m1 =5*10^-4 kg , u1 =724 m/s

From conservation of momentum

(5*10^-4*724) +0 = (48 - 0.015 +0.0005)v

v = 0.00754 m/s

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