If a body collides inelastically with another | vedclass

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(B) Let $u_1$ be the initial speed of the first body and $u_2 = 0$ be the initial speed of the second body.Let $v_1$ and $v_2$ be their respective spe

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$\frac{1-e}{1+e}$

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(B) Let $u_1$ be the initial speed of the first body and $u_2 = 0$ be the initial speed of the second body.Let $v_1$ and $v_2$ be their respective speeds after the collision.By the law of conservation of linear momentum: $m u_1 + m(0) = m v_1 + m v_2$,which simplifies to $u_1 = v_1 + v_2$.The coefficient of restitution $e$ is defined as $e = \frac{v_2 - v_1}{u_1 - u_2} = \frac{v_2 - v_1}{u_1}$.Substituting $u_1 = v_1 + v_2$ into the equation for $e$: $e = \frac{v_2 - v_1}{v_1 + v_2}$.Rearranging the terms: $e(v_1 + v_2) = v_2 - v_1 \implies ev_1 + ev_2 = v_2 - v_1$.Grouping $v_1$ and $v_2$ terms: $v_1(1 + e) = v_2(1 - e)$.Therefore,the ratio of their speeds is $\frac{v_1}{v_2} = \frac{1 - e}{1 + e}$.

If a body collides inelastically with another body of the same mass initially at rest,what will be the ratio of their speeds after the collision?

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