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Q.
The celing of a long hall is $20\, m$ high. What is the maximum horizontal distance that a ball thrown with a Speed of $40 \,ms ^{-1}$ can go without hitting the ceiling of the hall $\left(g=10 ms ^{-2}\right)$
Solution:
Here, $H=20 \,m \,\,\,u=40 \,ms ^{-1}$
Suppose the ball is thrown at an angle $\theta$ with the horizontal
Now $H=\frac{u^{2} \sin \theta}{2 g} $
$\Rightarrow 20=\frac{(40)^{2} \sin ^{2} \theta}{2 \times 10}$
Or $\sin \theta=0.5 \Rightarrow \theta=30^{\circ}$
Now, $R=\frac{u^{2} \sin 2 \theta}{g}$
$=\frac{(40)^{2} \times \sin 60^{\circ}}{10}$
$=138.56 \,m$