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. $25^{°}$
• B. $30^{°}$
• C. $45^{°}$
• D. $60^{°}$

Answer 1

Answer: (B)

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