Question

A bullet with muzzle velocity of 100 m/s is to be shot at a target 30 m away in same horizontal line. Height H above the target where the gun must be aimed so that bullet hits target is $[g=10m/s^2]\text{and H is in meter}$ (Assume the angle of projection ($\theta$)turns out to be so small that $\sin \theta =\tan \theta =\theta$)

Answer 1

$R=\frac{v^{2}sin2\theta }{g}$

$30=\frac{{10}^{4}sin2\theta }{10}\Rightarrow sin2\theta =\frac{300}{{10}^4}$

$sin2\theta =2\theta =0.03\Rightarrow \theta =0.015$

$tan\theta =\theta =\frac{H}{30}\Rightarrow H=30\times \theta$

$H=30\times 0.015=0.45m$