Question

A projectile is thrown with an initial velocity (a$\hat{i}$ + b$\hat{j}$) m/s. If the range of projection is twice the maximum height reached by it, then

• A. $b=\frac{a}{2}$
• B. $b=a$
• C. $b=2a$
• D. $b=3a$

Answer 1

Answer: (C)

$b=2a$

$\overrightarrow{u}=a\hat{i}+b\hat{j}$
Given, $R=2H$
$\Rightarrow \frac{u^{2}sin2\theta }{g}=\frac{2u^{2}si{n}^2\theta }{2g}$
$\Rightarrow \frac{2si{n}^2\theta }{2}=sin2\theta$
$\Rightarrow si{n}^2\theta =2sin\theta cos\theta$
$\Rightarrow tan\theta =2$
$\Rightarrow \frac{b}{a}=2;b=2a$