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Q.

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

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answer is 5.

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Detailed Solution

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

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