Question

If the speed of a projectile at maximum height is half of the initial speed of projection, Horizontal range will be:-

• A. $\sqrt{3}{u}^2/2g$
• B. $u^2/3g$
• C. $3u^2/2g$
• D. $3u^2/g$

Answer 1

The correct option is A $\sqrt{3}{u}^2/2g$

At the maximum height,

$ucos\theta =\frac{u}{2}$

$cos\theta =\frac{1}{2}$

$\theta ={60}^0$

Horizontal range,

$R=\frac{u^{2}sin2\theta }{g}$

$R=\frac{u^{2}sin{120}^0}{g}$

$R=\frac{\sqrt{3}{u}^2}{2g}$

The correct option is A.