Physics - Center of Mass Question with Solution | TestHub

Let $u_1$ be the initial speed of the smaller body before collision. 

Let $v$ be the final speed of the bigger body after collision.

Applying conservation of linear momentum,

$$\begin{gathered} 1\times u_1+0=-2+3v \\ \Rightarrow u_1=-2+3v ...\left(1\right) \end{gathered}$$ 

We know, coefficient of restitution for elastic perfectly collision is $1$.

 $$\begin{gathered} \Rightarrow 1=\frac{v+2}{u_1} \\ \Rightarrow v+2=u_1 ...\left(2\right) \end{gathered}$$ 

Equating $\left(1\right) \mathrm{and} \left(2\right)$, we have

$u_1=4 \mathrm{m} {\mathrm{s}}^{-1}$.