Question

A projectile is thrown with an initial velocity of $v=a\hat{i}+b\hat{j}$. If the range of projectile is doubled, then find the maximum height reached by it.

• A. $b=2a$
• B. $b=3a$
• C. $b=12a$
• D. $b=4a$

Answer 1

The correct option is A $b=2a$

Angle of projection , $\theta =ta{n}^{-1}\frac{v_y}{v_x}=ta{n}^{-1}\frac{b}{a}$

$\therefore \tan \theta =\frac{b}{a}$.............. (i)

From formula $R=4H\cot \theta =2H$

$\Rightarrow \cot \theta =\frac{1}{2}\therefore \tan \theta =2$ [As $R=2H$ given ]...................(ii)

From Eqs (i) and (ii), $b=2a$