A body x when a momentum p collides with another identical stationary body why one dimensional
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Impulse on A =-Impulse on B
Impulse = change in momentum
Let $u_1$ be the initial velocity of A
$p= mu_1$
After collision let $v_1$ and $v_2$ be the velocities of A and B in the same direction.
$J= mv_2$ ---- (1)
$-J=mv_1-mu_1$
$J=mu_1-mv_1$
$J= p-mv_1$ ----(2)
$2J= p+m(v_2-v_1)$
$2J-p= m(v_2-v_1)$
$\large\frac{v_2-v_1}{u_1}$$=e$
$\qquad= \large\frac{2J-p}{p}$
$\qquad= \large\frac{2J}{p}$$-1$
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