The ceiling of a long hall is $25\; m$ high. What is the maximum horizontal distance that a ball thrown with a speed of $40\; m/ s$ can go without hitting the ceiling of the hall ?
The ceiling of a long hall is $25\; m$ high. What is the maximum horizontal distance that a ball thrown with a speed of $40\; m/ s$ can go without hitting the ceiling of the hall ?
Speed of the ball, $u=40\, m / s$ Maximum height, $h=25 \,m$
In projectile motion, the maximum height reached by a body projected at an angle $\theta,$ is given by the relation:
$h=\frac{u^{2} \sin ^{2} \theta}{2 g}$
$25=\frac{(40)^{2} \sin ^{2} \theta}{2 \times 9.8}$
$\sin ^{2} \theta=0.30625$
$\sin \theta=0.5534: . \theta=\sin ^{-1}(0.5534)=33.60^{\circ}$
Horizontal Range $R=\frac{u^{2} \sin 2 \theta}{g}$
$=\frac{(40)^{2} \times \sin 2 \times 33.60}{9.8}$
$=\frac{1600 \times \sin 67.2}{9.8}$
$=\frac{1600 \times 0.922}{9.8}=150.53\, m$
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