Question

The ceiling of a hall is 40 m 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 ${30}^{\circ }$

Here, $u=56m{s}^{-1}$
Let $\theta$ be the angle of projection with the horizontal to have maximum range, with maximum height = 40 m
Maximum height, $H=\frac{u^{2}si{n}^2\theta }{2g}$
$40=\frac{(56{)}^{2}si{n}^2\theta }{2\times 9.8}$
$si{n}^2\theta =\frac{2\times 9.8\times 40}{(56{)}^2}=\frac{1}{4}$ or $sin\theta =\frac{1}{2}$
$\theta =si{n}^{-1}\left(\frac{1}{2}\right)={30}^{\circ }$