Question

The celing of a long hall is $20m$ high. What is the maximum horizontal distance that a ball thrown with a Speed of $40m{s}^{-1}$ can go without hitting the ceiling of the hall $\left(g=10m{s}^{-2}\right)$

• A. 138.56 m
• B. 149 m
• C. 135.3 m
• D. 132.76 m

Answer 1

Answer: (A)

Here, $H=20mu=40m{s}^{-1}$
Suppose the ball is thrown at an angle $\theta$ with the horizontal
Now $H=\frac{u^2\sin \theta }{2g}$
$\Rightarrow 20=\frac{(40{)}^2{\sin }^2\theta }{2\times 10}$
Or $\sin \theta =0.5\Rightarrow \theta =30^{\circ }$
Now, $R=\frac{u^2\sin 2\theta }{g}$
$=\frac{(40{)}^2\times \sin 60^{\circ }}{10}$
$=138.56m$