Question

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses $m,2m$ and $m$, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m/s) of the object C.

Answer 1

After 1st collision
$m{v}_A=m{v}_A^{\prime }+2m{v^{\prime }}_B$

$-1=\frac{{v^{\prime }}_B-{v^{\prime }}_A}{0-v_A}\Rightarrow {v^{\prime }}_B=6m/s$

After the 2nd collision
$2m{v}_B^{\prime }=(2m+m{)}_{V_C}\Rightarrow v_C=\frac{2}{3}{v}_B^{\prime }\Rightarrow v_C=4m/s$