The ceiling of a long hall is 25 m hight . What is the maximum horizontal distance that a ball thrown with a speed of 40 `mn^(-1)` can go without hitting the ceiling of the hall ?

Explanation

Here, u = 40 `ms^(-1)` , H = 25 m R = ?
Let `theta` be the angle of projection with the horizontal direction to have the maximum range , with maximum height = 25 m .
Maximum height, `H = 25 = (u^(2) sin^(2) theta)/(2g)`
`= ((40)^(2) sin^(2) theta)/(2 xx 9.8)`
or sin `theta = ((25 xx 2 xx 9 .8)/(40^(2))) = = 0 . 5534 `
` = sin 333.6^(@) ` or ` theta = 33 . 6^(@)`
Horizontal range, R ` = (u^(2) sin 2 theta)/(g)`
`=((40)^(2) xx sin (2 xx 33 . 6^(@)))/(9 . 8 )`
`= (1600 xx 0 . 9219)/(9 . 8) = 150 . 5 m `