Question

The maximum height attained by projectile is increased by 10% by changing the angle of projection, without changing the speed of projection. The percentage increase in the time of flight will be

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

Answer 1

Answer: (D)

$5$

$Given:$ Maximum height attained by projectile is increased by$10\%$.

$Solution:$

Let $h$ be the maximum height attained by the projectile. Then

$h=\frac{u^2{\sin }^2\theta }{2g}$

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

$\therefore \frac{R}{h}=\frac{u^2\sin 2\theta }{g}=/\frac{u^2{\sin }^2\theta }{2g}$

$=\frac{2\sin \theta \cos \theta }{\left({\sin }^2\theta \right)/2}$

$=4\cot \theta$

Therefore, $\frac{\Delta R}{R}=\frac{\Delta h}{h}$

Hence, percentage increase in $R$

percentage increase in height $h=5\%$

$So,the$ $correct$ $option:D$