The ceiling 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 `(g=10 ms^(-2))`

Explanation

Here `H=20 m, u=40 ms^(-1)`. Suppose the ball is thrown at an angle `theta` with the horizontal.
Now `H=(u^(2) sin^(2) theta)/(2g) rArr 20=((40)^(2) sin^(2) theta)/(2xx10)`
or `sin theta=0.5 " " or theta=30^(@)`
Now `R=(u^(2)sin 2 theta)/(g)=((40)^(2)xx sin 120^(@))/(10)`
`=((40)^(2)xx0.866)/(10)=138.56 cm`