An object of mass M is much heavier than anot | vedclass

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(A) From the law of conservation of momentum:$Mv + m 	imes 0 = Mv_1 + mv_2$$\Rightarrow M(v - v_1) = mv_2 \dots (i)$From the law of conservation of k

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$2v$

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(A) From the law of conservation of momentum:$Mv + m 	imes 0 = Mv_1 + mv_2$$\Rightarrow M(v - v_1) = mv_2 \dots (i)$From the law of conservation of kinetic energy (since the collision is elastic):$\frac{1}{2}Mv^2 + 0 = \frac{1}{2}Mv_1^2 + \frac{1}{2}mv_2^2$$\Rightarrow M(v^2 - v_1^2) = mv_2^2 \dots (ii)$Dividing equation $(ii)$ by $(i)$:$\frac{M(v - v_1)(v + v_1)}{M(v - v_1)} = \frac{mv_2^2}{mv_2}$$v + v_1 = v_2 \dots (iii)$Solving equations $(i)$ and $(iii)$ for the final velocity of the light object $(v_2)$:$v_2 = \frac{2Mv}{M + m}$Since $M \gg m$,we can approximate $M + m \approx M$:$v_2 = \frac{2Mv}{M} = 2v$.

An object of mass $M$ is much heavier than another object of mass $m$. The heavy object moving with speed $v$ undergoes an elastic collision with the light object at rest. What will be the speed of the light object after the collision?

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