Question

A gun projects a ball at the angle of ${45}^{\circ }$ with the horizontal. If the horizontal range is $39.2m$, then the ball will rise to

• A. $9.8m$
• B. $4.9m$
• C. $2.45m$
• D. $19.6m$

Answer 1

The correct option is A $9.8m$

Horizontal range $=\frac{u^2\sin 2\alpha }{g}=39.2$
$\Rightarrow \frac{u^2\sin {90}^{\circ }}{9}=39.2$
$\Rightarrow \frac{u^2}{g}=39.2$
$\therefore$ Greatest height reached $=\frac{u^2{\sin }^2\alpha }{2g}$
$=\frac{39.2}{2}.{\sin }^2{45}^{\circ }=\left(19.6\right).\left(\frac{1}{2}\right)=9.8m$.