Question

The ceiling of a long hall is $25m$ 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?

Answer 1

H${}_{max}$ =$\frac{{\mu }^{2}si{n}^2\theta }{g}$=25m

=$\frac{(40{)}^2\times si{n}^2\theta }{9.8}$ =25m

sin${}^2\theta$ =0.153125

$\theta$=23${}^0$

Now, T$\frac{2\mu sin\theta }{g}$ =$\frac{2\times 40\times 0.4}{9.8}$ =3.19sec

Now, x = $\mu cos\theta \times T$

=40x cos(23${}^0$) x 3.19

x= 117.62 m

Therefore , maximum horizontal distance is 117.62 metres.