The ceiling of a long hall is 20 m high. What is the maximum horizontal distance that a ball thrown with a speed of `40ms^(-1)` can-go without hitting the ceiling of the hall? `(g = 10 ms^(-1))`

Explanation

Given H = 20 m , ` V_0 = 40 ms^(-1)`
Maximum horizontal
distance ` = (V_0^2 sin 2 theta)/(g) = 20`
i.e., ` (40)^2 sin^2 theta = 20 xx 2 xx 10 `
` therefore sin^2 theta = (20 xx 20)/(40 xx 40) = 1/4`
i.e., ` sin theta = 1/2 " or " theta = 30^@`
Hence horizontal range ` = (40 xx 40 xx sin ( 2 xx 30^@ ))/(10) = 160 xx sin 60^@ = 160 xx 0.08660 = 138.56 m `