Question

A rifle shoots a bullet with a muzzle velocity of 400 m/sec at a small target 400 metre away. The height above the target at which the bullet must be aimed to hit the target is: (Take g =10ms^-2)

Moderate

Solution

Time taken by bullet to reach the target
$= \frac{distance}{velocity} = \frac{distance}{ucos θ}$
As $θ$ is very small, cos $θ$ = 1
$Time = \frac{distance}{u} = \frac{400}{400} = 1 \sec$
Vertical deflection of bullet
$= \frac{1}{2} {gt}^{2} = \frac{1}{2} \times 10 \times (1)^{2} = 5 metre$

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