Question

The horizontal range and maximum height attained by a projectile are $R$ and $H$, respectively. If a constant horizontal acceleration $a=\frac{g}{4}$ is imparted to the projectile due to wind, then its horizontal range and maximum height will be

• A. $(R+H),\frac{H}{2}$
• B. $(R+H),2H$
• C. $(R+2H),H$
• D. $(R+H),H$

Answer 1

The correct option is D $(R+H),H$

$H=\frac{u^2{\sin }^2\theta }{2g},R=\frac{u^2\sin 2\theta }{g}$ Maximum height will be same because acceleration $a=g$ is in horizontal direction.
$R^{\prime }=u\cos \theta T+\frac{1}{2}a{T}^2$
Since time of flight, $T=\frac{2u\sin \theta }{g}$
$\therefore R^{\prime }=u\cos \theta \left(\frac{2u\sin \theta }{g}\right)+\frac{1}{2}\frac{g}{4}{\left(\frac{2u\sin \theta }{g}\right)}^2$
$\therefore R^{\prime }=R+\frac{1}{2}\frac{g}{4}{\left(\frac{2u\sin \theta }{g}\right)}^2=R+H$