A hunter aims a gun at a monkey hanging from a tree some distance away. The monkey drops from the branch at the moment he fires the gun hoping to avoid the bullet. Explain why the monkey made a wrong move.

Explanation

Suppose the gun situated at O directed towards the monkey at position M . Let bullet leaves the barrel of the gun with velocity u at an angle `theta` with the horizontal . Let bullet crosses the vertical line MB at A after line t. Horizontal distance travelled .
`OB = x= u cos theta t or " " t= (x)/(u cos theta)`
For motion of bullet from O to B, the vertical height
`AB = u sin theta t - (1)/(2) "gt"^(2) = u sin theta((x)/(u cos theta)) - (1)/(2)"gt"^(2)`
` =x tan theta - ("gt"^(2))/(2)" "..........(i)`
Also `MB = x tan theta`
Now `y= MA = MB -AB = x tan theta - ( x tan theta - ("gt"^(2))/(2)) = (1)/(2)gt^(2)`
Thus , in time t the bullet passes through A a vertical distance ` (1)/(2) "gt"^(2) ` below M.
Thus , the bullet and the monkey will always reach at pont A at the same time.