Question

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

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

Answer 1

Answer: (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, $H=\frac{u^{2}si{n}^2\theta }{2g}$
$40=\frac{(56{)}^{2}si{n}^2\theta }{2X9.8}$

$sin2\theta =\frac{2\times 9.8\times 40}{(56{)}^2}=\frac{1}{4}$

or $sin\theta =\frac{1}{2}$

or $\theta =si{n}^{-1}\left(\frac{1}{2}\right)={30}^{\circ }$