Question

A projectile is thrown with an initial velocity of $ \overrightarrow{v} = (pi + q\hat{j})\, m/s $ . If the range of the projectile is double the maximum height reached by it, then

• A. $ p = 2q $
• B. $ q = 4p $
• C. $ q = 2p $
• D. $ q = p $

Answer 1

Answer: (C)

Given, $v = pi + qj$
According to equation
$2H = R$
$\frac{u^2\,\sin^2 \,\theta}{2g} = \frac{u^2\,\sin\,2\theta}{g}$
$\sin^2 \,\theta = 2\,\sin\,\theta\,\cos\,\theta$
$\tan\,\theta = 2$
$ \tan\,\theta = \frac{q}{p}$
$\therefore 2 = \frac{q}{p}$
$q = 2p$