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 $56\,ms^{-1}$ without hitting the ceiling of the hall is

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

Answer 1

Answer: (B)

Here, $u = 56\,ms^{-1}$
Let $\theta$ be the angle of projection with the horizontal to have maximum range, with maximum height $= 40\,m$
Maximum height, $H=\frac{u^{2}\,sin^{2}\,\theta}{2g}$
$40=\frac{\left(56\right)^{2}\,sin^{2}\,\theta}{2\times9.8}$
$sin^{2}\,\theta =\frac{2\times9.8\times40}{\left(56\right)^{2}}=\frac{1}{4}$ or
$sin\,\theta =\frac{1}{2}$ or
$\theta=sin^{-1}\left(\frac{1}{2}\right)$
$=30^{°}$