Question

A bullet with muzzle velocity $500\text{m/s}$ is to be shot at a target $1000\text{m}$ away in the same horizontal line. At what height above the target, a rifle must be aimed so that the bullet will hit the target ?

• A. $30\text{m}$
• B. $20\text{m}$
• C. $65\text{m}$
• D. $40\text{m}$

Answer 1

The correct option is B $20\text{m}$


When the bullet hits target $P$, it's horizontal range will be $1000\text{m}$
$\Rightarrow$ Since $u_y=0$, $u_x=u=500\text{m/s}$

$\therefore$ Time of flight for bullet:
$T=\sqrt{\frac{2h}{g}}............i$

Now kinematic equation in X-direction:
$OP=\left(u_x\right)\times T.........ii$

$\Rightarrow 1000=500\times \sqrt{\frac{2h}{g}}$
$\Rightarrow \frac{2h}{g}=2^2=4$
$\therefore h=20\text{m}$

Hence, $h$ is the required height at which a rifle should be fired to hit the target at $P$.