Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. These have…
Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. These have masses $m, 2 m$ and $m$, respectively. The object $A$ moves towards $B$ with a speed $9 \mathrm{~ms}^{-1}$ 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 $\mathrm{ms}^{-1}$ ) of the object $C$.
Solution
After elastic collision,
$
\begin{aligned}
v_A^{\prime} & =\left(\frac{m-2 m}{m+2 m}\right)(9)+\frac{2(2 m)}{m+2 m}(0) \\
& =-3 \mathrm{~ms}^{-1}
\end{aligned}
$
Now from conservation of linear momentum after all collisions are complete,
$
\begin{array}{rlrl}
m\left(+9 \mathrm{~ms}^{-1}\right) & =m\left(-3 \mathrm{~ms}^{-1}\right)+3 m\left(v_C\right) \\
& \text { or } \quad v_C & =4 \mathrm{~ms}^{-1}
\end{array}
$
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