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)/(2 xx 10)`
or, `sin theta = 0.5` or, `theta = 30^(@)`
Now, `R=(u^(2)sin 2theta)/g =((40)^(2) xx sin 120^(@))/10`
`=((40)^(3) xx 0.866)/10 = 138.56` cm