Q has equipped James Bond\'s 1963 Aston Martin with rocket launchers just beneat

Question

Q has equipped James Bond's 1963 Aston Martin with rocket launchers just beneath each headlight. Under attack by approaching KGB assassins, Agent 007 fires two rockets simultaneously while backing up with velocity v1 = -v1i. Each rocket has mass m and launch velocity v3 = v3i relative to the car. After the rockets are fired, the aston Martin (mass M) moves with velocity v2 = -v2i.

1. What is the absolute velocity of the rockets after they are fired?

2. Calculate the Asont Martin's post-firing speed, v2.

3. Compute the change in total kinetic energy of the Aston Martin and the rockets as a function of M, m and vr. Explain why the total kinetic energy increases.

Explanation / Answer

Conservation of Momentum we have -(M+2m)*v1 = -M*v2 + 2m*(v3 + v2) 1)So absolute velocity is M(v2)-M+2m(v1)/2m 2)v2 = ((M+2m)*v1 + 2*m*v3)/(M-2m) 3)Total kinetic Energy Change is 0.5*[2m*(v3+v2)*(v3+v2) + M*v2*v2 - (M+2m)*v1*v1] = 0.5[2m*(v3+v2+v1)*(v3+v2-v1) + M(v2*v2 - v1*v1)] After some calculation it is found that it is 0.5*2*m*M/(M+2m)*vr*vr The total kinetic energy increases due the fact that for the rockets to launch extra energy is to be fed into the system

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