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?

A hunter aims his gun and fires a bullet directly at a monkey on a tre

1.	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?
Answer» Solution :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.