A rocket of mass m initially at rest carries a quantity of f

A rocket of mass m initially at rest carries a quantity of fuel of mass M. It converts an amount M1 of this fuel into energy which it uses to throw the remaining mass of the fuel M_2 (M = M_1 + M_2) backward. Show that the kinetic energy, K, acquired by the rocket is

Solution

k=p2/2m here p2 =m2v2 then p=mv if we squqres it becomes m2v2 k=p2/2m and m1 is released out as energy and we take in to account only M2 and we should use (M-M2) and for m=M+m we should take. then k=(M² -M²_{2) C}^2/   2(M+m)