A shell of mass 200, g is ejected from a gun | vedclass

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(C) Let $m = 0.2\, kg$ be the mass of the shell and $M = 4\, kg$ be the mass of the gun. Let $v$ be the velocity of the shell and $V$ be the recoil ve

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$100$

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(C) Let $m = 0.2\, kg$ be the mass of the shell and $M = 4\, kg$ be the mass of the gun. Let $v$ be the velocity of the shell and $V$ be the recoil velocity of the gun.By the law of conservation of momentum,$mv = MV$,so $V = (m/M)v$.The total energy generated by the explosion is equal to the sum of the kinetic energies of the shell and the gun:$E = \frac{1}{2}mv^2 + \frac{1}{2}MV^2$Substituting $V = (m/M)v$:$E = \frac{1}{2}mv^2 + \frac{1}{2}M(\frac{m}{M}v)^2 = \frac{1}{2}mv^2 (1 + \frac{m}{M})$Given $E = 1.05\, kJ = 1050\, J$,$m = 0.2\, kg$,and $M = 4\, kg$:$1050 = \frac{1}{2} 	imes 0.2 	imes v^2 	imes (1 + \frac{0.2}{4})$$1050 = 0.1 	imes v^2 	imes (1 + 0.05)$$1050 = 0.1 	imes 1.05 	imes v^2$$1050 = 0.105 	imes v^2$$v^2 = \frac{1050}{0.105} = 10000$$v = 100\, m/s$.

$A$ shell of mass $200\, g$ is ejected from a gun of mass $4\, kg$ by an explosion that generates $1.05\, kJ$ of energy. The initial velocity of the shell is .............. $m/s$.

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