Question

A gun (mass = $M$ ) fires a bullet (mass = $m$ ) with speed $V_{r}$ relative to the barrel of the gun which is inclined at an angle of $60^\circ $ with horizontal. The gun is placed over a smooth horizontal surface. Find the recoil speed of the gun.

• A. $V=\frac{1}{2}\frac{\left(\textit{mV}\right)_{\text{r}}}{\left(\textit{m} + \textit{M}\right)}$
• B. $V=\frac{1}{2}\frac{\left(\textit{mV}\right)_{\text{r}}}{\left(\textit{m} - \textit{M}\right)}$
• C. $V=\frac{1}{2}\frac{\left(\textit{MV}\right)_{\text{r}}}{\left(m + M\right)}$
• D. None of the above

Answer 1

Answer: (A)

Using conservation of linear momentum in the horizontal direction.
$\textit{m}\left(\left(\textit{V}\right)_{\text{r}} \text{cos} \text{60°} - \textit{V}\right)\text{= }\textit{MV}$
$\frac{\textit{mV}_{r} \text{cos 60}^{\text{o}}}{\textit{m} + \textit{M}}=\textit{V}$
$\textit{V}=\frac{1}{2}\frac{\left(\textit{mV}\right)_{r}}{\left(\textit{m} + \textit{M}\right)}$