Question

A horizontal rifle is fired at a target, the barrel of the rifle is pointed directly at the target, but the bullet strikes $0.05m$ below the target. If the speed of the bullet is $650m{s}^{-1}$, then determine the horizontal separation between the front of the rifle and the target [Take $g=10m{s}^{-1}$].

Answer 1

Step 1: Given data

Distance of target from the bullet, $s=0.05m$.

Speed of bullet, $v=650m{s}^{-1}$.

Acceleration due to gravity, $g=10m{s}^{-1}$.

Step 2: Find the time required for the bullet to hit

Using the equation of motion in a y plane $\mathit{s}\mathbf{=}\mathit{u}\mathit{t}\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{1}}{\mathbf{2}}\mathit{a}{\mathit{t}}^{\mathbf{2}}$:

$\Rightarrow 0.05=0+\frac{1}{2}\left(10\right)t^2$

$$\begin{gathered} \Rightarrow 0.05=0+5t^2 \\ \Rightarrow t^2=\frac{0.05}{5} \\ \Rightarrow t^2=0.01 \\ \Rightarrow t=\sqrt{0.01} \end{gathered}$$

$\Rightarrow t=0.1s$

Step 3: Find the horizontal separation between the front of the rifle and the target.

The formula used to calculate horizontal separation (Range) is $\mathit{R}\mathbf{=}\mathit{s}\mathbf{\times }\mathit{t}$

$\Rightarrow R=650\times 0.1$

$\Rightarrow R=65m$

Hence, the horizontal separation between the front of the rifle and the target is $\mathbf{65}\mathbf{}\mathit{m}$.