Question

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 ?

Answer 1

Given,

$u=40m/s$

$H=25m$

$g=10m/a^2$

The maximum height in projectile motion,

$H=\frac{u^{2}si{n}^2\theta }{2g}=25m$

$si{n}^2\theta =\frac{25\times 2g}{u^2}$

$si{n}^2\theta =\frac{25\times 2\times 10}{40\times 40}$

$sin\theta =\sqrt{0.3125}=0.55$

$\theta =si{n}^{-1}\left(0.5\right)={33.98}^0$

Maximum Horizontal range in projectile motion,

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

$R=\frac{40\times 40sin(2\times 33.98)}{10}$

$R=148.32m$