Question

A rifle shoots a bullet with a muzzle velocity of $400m{s}^{-1}$ at a small target $400$ m away. The height above the target at which the bullet must be aimed to hit the target is (g = $10m{s}^{-2}$).

• A. $1m$
• B. $5m$
• C. $10m$
• D. $0.5m$

Answer 1

The correct option is B $5m$

Time taken by bullet to reach the target is
$\frac{Distance}{Velocity}=\frac{Distance}{u\cos \theta }$, As $\theta$ is very small, $\cos \theta =1$
$Time=\frac{Distance}{u}=\frac{400}{400}=1s$
Vertical deflection of bullet is
$\frac{1}{2}g{t}^2=\frac{1}{2}\times 10\times (1{)}^2=5m$.