Will the Bullet Hit the Falling Monkey?

[salhayek]

Homework Statement

The hunter is pointing his gun at angle theta to the horizontal. If the monkey releases his grip at the same instant the hunter fires the gun, show that the monkey will be struck by the bullet after falling a distance delta y given by:

Delta Y=g/2(R^2+H^2/V^2)
where R is the distance between the hunter and the tree,H is the height the monkey is away from the ground, delta y is where the bullet and the monkey meet, and v is the speed of the bullet when leaving the gun. Neglect air resistance.

Homework Equations

Delta Y=g/2(R^2+H^2/V^2)

The Attempt at a Solution

I tried looking at the x and y directions independently but have had no luck so far

 

[spacelike]

Well I worked it out and it doesn't really sit well with me.

It's a bit hard to figure out the assumption they are making so I'll just tell you what it is, I don't see how you can solve this without making this assumption.

They are assuming that the hunter is originally pointing his gun perfectly straight at the monkey.
Therefore you can make use of a right triangle where the legs are R and H and the hypotenuse is \sqrt{R^{2}+H^{2}}, and the angle \theta is also defined based on this triangle

That should be a big help, I don't see why they would leave out that crucial information. You can sort of solve it without that but you won't get exactly the form of DeltaY they have unless you use it.

Also, another hint is that the time shall be governed by how long it takes the bullet to travel in the X-direction a distance R.
Because the x-component is not disturbed at all, and we know that if the bullet is any more to the left or right of exactly where it is after traveling a distance R then it would be impossible to hit the monkey.
So find the time for the bullet to travel in the x-direction a distance R and that is the time the monkey will be hit. Then just find how far it falls.

 

[Legendon]

It is also important to note that the path of the bullet crosses the vertical axis of the monkey.

 

[salhayek]

Thanks so much for the help! I tried to work this out with the d=Vot+1/2at^2 but I just doesn't seem to work. How do I go about this?

 

[spacelike]

well for the x-component of the bullet there is no "a", so you just have d=Vot