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

Explanation

Maximum height `h_("max") = 25m`, Horizontal range, R=?
Velocity of projection, v=`40ms^(-1)`
We know that `h_("max") = (v^(2)sintheta)/(2g)`
or `sin^(2)theta= (25 xx 2 xx 9.8)/(40 xx 40) = 0.30625` or `sintheta = 0.5534`
`theta= sin^(-1)(0.5534)=33.6^(@)`
Again, `R= (v^(2)sin2theta)/(g) = (40 xx 40sin67.2^(@))/(9.8)`
or `R=100/9.8 xx 0.9219 m = 150.5m`.