# Will the Bullet Hit the Falling Monkey?

• salhayek
In summary: Vot+1/2at^2. then you can use the Pythagorean theorem to find the distance between the y-axis and the 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

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.

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

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?

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

## 1. What is the "Monkey and Hunter Question"?

The "Monkey and Hunter Question" is a thought experiment designed to explore the concept of projectile motion and the influence of gravity on falling objects.

## 2. Who came up with the "Monkey and Hunter Question"?

The "Monkey and Hunter Question" was first proposed by Italian physicist Galileo Galilei in the 16th century.

## 3. How does the "Monkey and Hunter Question" relate to science?

The "Monkey and Hunter Question" is used to demonstrate the principles of projectile motion and gravity, which are important concepts in the field of physics.

## 4. What is the purpose of the "Monkey and Hunter Question"?

The purpose of the "Monkey and Hunter Question" is to challenge our understanding of how gravity affects falling objects and to encourage critical thinking about the laws of motion.

## 5. Can the "Monkey and Hunter Question" be applied to real-life situations?

Yes, the principles demonstrated in the "Monkey and Hunter Question" can be applied to real-life situations, such as understanding the trajectory of a ball being thrown, or the flight path of a projectile.

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