"Kinetic Energy and Collisions"
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Linear momentum conservation Law is required to answer this question.
In the absense of external forces, the linear momentum of a system is conserved.
Linear momentum of a body with mass m is mV, were V is the velocity of the body.
The linear momentum of rocket-gas system prior to expulsion is 0 because it is at rest.
The linear momentum of rocket-gas system after the expulsion is (M-m)V - mU. Here M is the mass of the rocket, m is the mass of the gas, V is the velocity of the rocket (5.7 m/s) and U is the unknown velocity of the gas, which is opposite in direction to V.
Since mass of gas m is thousand times smaller than mass of rocket M, it can be neglected in expression M-m. So we can write the momentum of the system after the expulsion as
MV - mU = 0.
From here U = MV/m = 2.04 * 10 ^6 * 5.7 / (3.7 * 10^3) m/s =
= 3.14* 10 ^3 m/s
The exhaust gas leaves the rocket with the velocity of 3.14*10^3 m/s.
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