Consider the situation as shown.

When a ball is thrown aiming the monkey, at the same time the monkey drops himself. Will the ball hit the monkey ?

Explanation

Taking `O` as origin, the ball will strike the monkey if after time `t`, the coordinates of ball and monkey are same. After time `t`,
Ball: `x_(1) = d = u cos theta t rArr t = (d)/(u cos theta)`
`y_(1) = x tan theta - (g x^(2))/(2 u^(2) cos^(2) theta) = d tan theta - (g d^(2))/(2u^(2) cos^(2) theta)`
Monkey: `x_(2) = d`
`y_(2) - d tan theta - (1)/(2) g t^(2)`
`= d tan theta - (g d^(2))/(2 u^(2) cos^(2) theta)`
`x_(1) = x_(2), y_(1) = y_(2)`

A ball aimed at the initial position of monkey always hits it, whatever be the value of `u`. In the absence of gravity, the monkey remains at its position and the ball will move in straight line. In the presence of gravity, both the ball and the monkey will fall by `(1)/(2) g t^(2)`.