Question

In a projectile motion if a person wants to increase the maximum height to $2$ times but simultaneously want to decrease the range same number of time. He can achieve it by increasing tan of angle of projection by ______ times

• A. $4$
• B. $5$
• C. $6$
• D. $1$

Answer 1

The correct option is A $4$

Range of projectile is given by $R=\frac{u^{2}Sin2\theta }{g}$

And maximum height is $H=\frac{u^{2}Si{n}^2\theta }{2g}$

If $\frac{R_2}{R_1}=\frac{1}{2}$ and $\frac{H_2}{H_1}=2$

Then $\frac{Sin2{\theta }_2}{Sin2{\theta }_1}=\frac{1}{2}$ and $\frac{Si{n}^2{\theta }_2}{Si{n}^2{\theta }_1}=\frac{2}{1}$

Dividing both we get $\frac{Tan{\theta }_2}{Tan{\theta }_1}=4$

So best possible answer is option A.