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(A) Let the mass of both bodies be $m$. The initial velocity of body $x$ is $u_x = p/m$ and body $y$ is $u_y = 0$.Impulse $J$ is the change in momentu

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$\frac{2J}{p} - 1$

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(A) Let the mass of both bodies be $m$. The initial velocity of body $x$ is $u_x = p/m$ and body $y$ is $u_y = 0$.Impulse $J$ is the change in momentum of the body. For body $x$,the impulse given by $y$ is $J = p_x' - p$,where $p_x'$ is the final momentum of $x$. Thus,$p_x' = p - J$.For body $y$,the impulse received is $J = p_y' - 0$,so $p_y' = J$.The coefficient of restitution $e$ is defined as $e = \frac{v_y' - v_x'}{u_x - u_y}$.Since $p = mv$,we have $v_x' = \frac{p-J}{m}$ and $v_y' = \frac{J}{m}$.Substituting these into the formula: $e = \frac{J/m - (p-J)/m}{p/m - 0} = \frac{J - p + J}{p} = \frac{2J - p}{p} = \frac{2J}{p} - 1$.

$A$ body $x$ with a momentum $p$ collides with another identical stationary body $y$ one-dimensionally. During the collision,$y$ gives an impulse $J$ to body $x$. Then,the coefficient of restitution is

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