Question

The ceiling of a hall is $40m$ high. For maximum horizontal distance, the angle at which the ball can 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

The correct option is B $30$

Range $R=\frac{v^{2}sin2\theta }{g}$

Height $H=\frac{v^{2}si{n}^2\theta }{2g}$

$40=\frac{{56}^2\times si{n}^2\theta }{2g}$

$\Rightarrow {\sin }^2\theta =0.25$

$\Rightarrow \sin \theta =0.5$

$\Rightarrow \theta ={30}^0$

If the angle is more than ${30}^0$, it will hit the ceiling

Range $R=\frac{v^2\sin 2\theta }{g}=\frac{{56}^2\sin {60}^0}{g}=271.5m$