Question

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

• A. a = 2b
• B. b = a
• C. b = 2a
• D. b = 4a

Answer 1

The correct option is C b = 2a

Angle of projection $\theta =ta{n}^{-1}\frac{b}{a}\therefore tan\theta =\frac{b}{a}$ .....(i)
From formula $R=4Hcot\theta =2H\Rightarrow cot\theta =\frac{1}{2}\therefore tan\theta =2$ ......(ii) [As R = 2H given]
From equation (i) and (ii) b = 2a