Question

The ceiling of a hall is $40m$ high. For maximum horizontal distance, the angle at which the ball may be thrown with a speed of $56m{s}^{-1}$ without hitting the ceiling of the hall is

• A. ${25}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${30}^{\circ }$

For the range to be maximum, $H\le 40m$
Since maximum height of a projectile, $H=\frac{u^2{\sin }^2\theta }{2g}$
$\Rightarrow 40=\frac{u^2{\sin }^2\theta }{2\times 9.8}$
${\sin }^2\theta =\frac{784}{56\times 56}$
$\Rightarrow {\sin }^2\theta =\frac{1}{4}$
$\Rightarrow \sin \theta =0.5$
$\Rightarrow \theta ={30}^{\circ }$