The initial speed of a bullet fired from a rifle is $630 \mathrm{~m} / \mathrm{s}$. The rifle is fired at…
The initial speed of a bullet fired from a rifle is $630 \mathrm{~m} / \mathrm{s}$. The rifle is fired at the centre of a target $700 \mathrm{~m}$ away at the same level as the target. How far above the centre of the target ?
$1.0 \mathrm{~m}$
$4.2 \mathrm{~m}$
$6.1 \mathrm{~m}$
$9.8 \mathrm{~m}$
Solution
Let ' $t$ ' be the time taken by the bullet to hit the target.
$
\begin{aligned}
&\therefore \quad 700 \mathrm{~m}=630 \mathrm{~ms}^{-1} t \\
&\Rightarrow t=\frac{700 \mathrm{~m}}{630 \mathrm{~ms}^{-1}}=\frac{10}{9} \mathrm{sec}
\end{aligned}
$
For vertical motion,
Here, $u=0$
$
\begin{aligned}
&\therefore h=\frac{1}{2} g t^2 \\
&=\frac{1}{2} \times 10 \times\left(\frac{10}{9}\right)^2
\end{aligned}
$
$
=\frac{500}{81} \mathrm{~m}=6.1 \mathrm{~m}
$
Therefore, the rifle must be aimed $6.1 \mathrm{~m}$ above the centre of the target to hit the target