Question

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 m` can go without hitting the ceiling of hall `(g=10 ms^(-2))` ?

Answer 1

`H le 25 `m
`rArr (u^(2))/( 2g) sin^(2) theta le 25 `m
`rArr sin^(2) theta le (25)/(80) = (5)/(sqrt(16))`
`rArr sin theta le (sqrt5)/( 4)`
For maximum range ` sin theta = sqrt((5)/(4))`
`tan theta = sqrt((5)/(11)) rArr R = (4H)/(tan theta) = ( 4xx 25)/( sqrt( 5//11)= 148. 32` m