A gun (mass = M ) fires a bullet (mass = m ) with speed V r relative to the barrel of the gun which is…

1. $V=\frac{1}{2}\frac{{\mathit{\text{mV}}}_{\text{r}}}{\left(\mathit{\text{m}}+\mathit{\text{M}}\right)}$
2. $V=\frac{1}{2}\frac{{\mathit{\text{mV}}}_{\text{r}}}{\left(\mathit{\text{m}}-\mathit{\text{M}}\right)}$
3. $V=\frac{1}{2}\frac{{\mathit{\text{MV}}}_{\text{r}}}{\left(m+M\right)}$
4. None of the above

Solution

Using conservation of linear momentum in the horizontal direction.

$\mathit{\text{m}}\left({\mathit{\text{V}}}_{\text{r}}\text{cos}\text{60°}-\mathit{\text{V}}\right)\text{= }\mathit{\text{MV}}$

$\frac{{\mathit{\text{mV}}}_r{\text{cos 60}}^{\text{o}}}{\mathit{\text{m}}+\mathit{\text{M}}}=\mathit{\text{V}}$

$\mathit{\text{V}}=\frac{1}{2}\frac{{\mathit{\text{mV}}}_{\mathit{r}}}{\left(\mathit{\text{m}}+\mathit{\text{M}}\right)}$

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