Question

The maximum height attained by a projectile is increased by $4\%$, keeping the angle of projection constant. The corresponding percentage increase in the horizontal range (in %) will be

Answer 1

If $H$ be the maximum height attained by the projectile and $R$ be the horizontal range of the projectile, then

$H=\frac{u^2{\sin }^2\theta }{2g}$ and $R=\frac{u^2\sin 2\theta }{g}$

$\frac{R}{H}=\frac{2\sin \theta \cos \theta }{\frac{\left({\sin }^2\theta \right)}{2}}=4\cot \theta$
As $\theta$ is said to be constant.
We can say $\frac{\Delta R}{R}=\frac{\Delta H}{H}$
$\therefore$ Percentage increase in $R$ = percentage increase in $H=4\%$