Question

A bullet is to be fired with a speed of 2000 ms^-1 to hit a target 200 m away on a level ground. If g = 10 ms ^-2, the gun should be aimed

Moderate

Solution

Let t be time taken by the bullet to hit the target.
$Range of the projectile = 200 = \frac{u^{2} \sin 2 θ}{g} 200 = \frac{{(2000)}^{2}}{g} \sin 2 θ \sin 2 θ = \frac{1}{2000}; θ = \frac{1}{4000} tanθ = \frac{1}{4000} = \frac{h}{R} = \frac{h}{200} h = \frac{1}{20} m = 5 cm$
$∴$ Gun should be aimed 5 cm above the target.

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