Question

The maximum height attained by a projectile is increased by $5\%$, keeping the angle of projection constant. The corresponding percentage increase in horizontal range will be

• A. $5\%$
• B. $10\%$
• C. $15\%$
• D. $20\%$

Answer 1

The correct option is A $5\%$

If $h$ be the maximum height attained by the projectile then
$h=\frac{u^2{\sin }^2\theta }{2g}$ and $R=\frac{u^2\sin 2\theta }{g},\frac{R}{h}=\frac{2\sin \theta \cos \theta }{\left({\sin }^2\theta \right)/2}=4\cot \theta$
Therefore $\frac{\Delta R}{R}=\frac{\Delta h}{h}$ (if $\theta$ is constant)
$\therefore$ Percentage increase in $R=$ percentage increase in $h=5\%$