A hunter aims his gun and fires a bullet directly at a monkey on a tree. At the instant the bullet leaves the barrel of the gun, the monkey drops. Will the bullet hit the monkey?

Explanation

Suppose the gun situated ato 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 time t. Horizontal distance travelled
`OB=x=ucos thetat` 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=xtan theta-(x tan theta-("gt"^(2))/2)=1/2"gt"^(2)`
Thus in the time t bullet through A a vertical distance `1/2"gt"^(2)` below M
The vertical distance through which the monkey fall in time t. `s=1/2"gt"^(2)`
Thus, the bullet and the monkey will always reach at point A at the same time.