Stage Rocket

A two stage rocket problem?

A two stage rocket moves in space at a constant velocity of 1500 m/s. the two stages are then separated by a small explosive charge. Immediately after the explosion the velocity of the 1200 kg upper stage is in 6500 m/s in the original direction. What is the speed and direction of the 2400 kg lower stage? How much additional kinetic energy is supplied by the explosion?

Using the conservation of momentum:

(m1 + m2)v = m1V1 + m2V2

m1 = 1200 kg
m2 = 2400kg
v = 1500 m/s
V1 = 6500 m/s
V2 = ?

V2 = ((m1 + m2)v – m1V1)/m2 = ((1200 + 2400)(1500) – (1200)(6500))/2400 = -1000 m/s

The speed is 1000 m/s
the direction is opposite the original (negative sign)

KE = 0.5mV^2

Gained kinetic energy = KE1 + KE2 – KE

0.5(1200)(6500)^2 + 0.5(2400)(-1000)^2 – 0.5(1200 + 2400)(1500^2)
= 2.25e10 J
= 2.25e7 kJ

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