# Monkey Bullet Proof: Analyzing Wrong Move

• MattWakes
In summary, the conversation discusses a problem where a hunter aims a gun at a monkey hanging from a tree branch. The monkey drops from the branch at the same time the gun is shot, hoping to avoid the bullet. The conversation explores the idea that the monkey may have made the wrong move because both the monkey and the bullet are affected by gravity and will eventually cross paths. The conversation also includes a discussion about converting units and using mathematical equations to prove that the monkey will be hit by the bullet.
MattWakes

## Homework Statement

A hunter on the ground aims his gun directly at a monkey hanging from a high tree branch some distance away. At the instant the gun is shot the monkey drops from the branch, hoping to avoid the bullet. Show analytically that the monkey made the wrong move. Ignore air resistance.

## The Attempt at a Solution

I'm at something of a loss here. I think we're trying to show that the time for the monkey to drop is less than the speed of the bullet. So I tried to solve for t in terms of h and g for the bullet, because of the t: sqrt (2h/g) of the monkey, but got nowhere. There are no units here.. Any ideas?

Both the monkey and the bullet are acted on by gravity. Thus even though the hunter aims up at the monkey, his bullet will eventually fall. Is it possible that the bullet therefore hits the monkey?

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Hi MattWakes! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

MattWakes said:
I'm at something of a loss here.

Me too! So it becomes a mind reading game...what was the lecturer likely thinking about when he set this question?

The gun is aimed "directly at the monkey" and it seems the monkey is some distance away. So I think we are to assume the hunter is failing to "aim high" to account for the bullet's path dipping due to gravity. (How was the monkey to know the hunter was such an amateur? He wasn't, so I don't really think we can accuse the monkey of misjudging his move.) It might carry more realism to say the hunter was using a bow and arrow, IMHO.

With this scenario, we have a clear picture to analyse. Is that better?

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If there were units, how would that help you solve the problem?

It appears the hunter has not aimed high to correct for the effect of gravity on the bullet. If the monkey hangs onto the branch the bullet might pass below him. If the monkey let's go he will fall into the path of the bullet. That's because the gun was pointed directly at him and both bullet and monket fall at same rate.

MattWakes said:

## Homework Statement

A hunter on the ground aims his gun directly at a monkey hanging from a high tree branch some distance away. At the instant the gun is shot the monkey drops from the branch, hoping to avoid the bullet. Show analytically that the monkey made the wrong move. Ignore air resistance.

## The Attempt at a Solution

I'm at something of a loss here. I think we're trying to show that the time for the monkey to drop is less than the speed of the bullet. So I tried to solve for t in terms of h and g for the bullet, because of the t: sqrt (2h/g) of the monkey, but got nowhere. There are no units here.. Any ideas?
You can't compare a time with a speed. They're different types of physical quantities and have different units. It makes sense to say 20 m/s is bigger than 10 m/s, but saying 20 m/s is bigger or smaller than 1 hour doesn't.

The problem statement implies the monkey gets hit by the bullet and wants you to show this. How do you express mathematically the monkey getting hit by the bullet? In other words, what quantities have to be equal when the bullet hits the monkey?

Thanks so much for the responses. They went a long way in demystifying this question. I now know that if the gun is pointed directly at the monkey, the force of gravity will act on both identically so that the bullet (I agree, should be arrow) and monkey will meet in midair. The quantities that must be equal for this to occur are height and time, right? By manipulating a constant acceleration equation, I get that the height for the monkey is h=gt^2/2. For the bullet, I'm having trouble writing that in the same units because of velocity; h=vit-gt^2/2. Does velocity matter? If the gun was fired at 1m/s, it wouldn't have a prayer of hitting the monkey.

What am I missing?

The help is greatly appreciated.

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MattWakes said:
the height for the monkey is h=gt^2/2. For the bullet, I'm having trouble writing that in the same units because of velocity; h=vit-gt^2/2.
Define those heights - where are they measured from?

The height for the monkey would be hm=h-.5gt^2
For the bullet, hb=vit-.5gt^2. I assume they're measured from the top of the tree branch?
If the heights were the same, the question would be proven. However, how do I convert vit to height?

MattWakes said:
The height for the monkey would be hm=h-.5gt^2
For the bullet, hb=vit-.5gt^2. I assume they're measured from the top of the tree branch?
If the heights were the same, the question would be proven. However, how do I convert vit to height?
Based on where the bullet was aimed, what would its height have been at that time t if there were no gravity?

Height h, the top of the branch, I expect. Then, vit converts to h and our quantities are equal. Yet how can I prove that mathematically?

MattWakes said:
Height h, the top of the branch, I expect. Then, vit converts to h and our quantities are equal. Yet how can I prove that mathematically?
Which bit do you think is in need of more rigour?

Hey, I figured it out. Using trig, tan(theta)=vy/vx=dy/dx. Dy=vydx/vx.
Vit, if I substitute for t, is vydx/vx. Therefore, h of bullet= h-1/2gt^2, just as the height of the monkey. Thx for the help

## 1. How does analyzing wrong moves in "Monkey Bullet Proof" help in understanding the game?

By analyzing wrong moves in "Monkey Bullet Proof", scientists can gain insight into the strategies and decision-making processes of players. This can help in understanding the overall gameplay and identifying areas for improvement.

## 2. What data is needed for analyzing wrong moves in "Monkey Bullet Proof"?

To analyze wrong moves in "Monkey Bullet Proof", scientists would need data on the moves made by players, the outcome of the game, and any relevant contextual information such as the player's skill level or the game mode.

## 3. Can analyzing wrong moves in "Monkey Bullet Proof" lead to any new discoveries or insights?

Yes, analyzing wrong moves in "Monkey Bullet Proof" can lead to new discoveries and insights about the game. By identifying patterns in wrong moves, scientists can uncover strategies that may not have been previously known or understood.

## 4. Are there any limitations to analyzing wrong moves in "Monkey Bullet Proof"?

One limitation of analyzing wrong moves in "Monkey Bullet Proof" is that it may not provide a complete picture of the game. It only focuses on the moves that were deemed incorrect, and may not take into account other factors such as luck or external influences.

## 5. How can the results of analyzing wrong moves in "Monkey Bullet Proof" be applied to other games or real-life scenarios?

The results of analyzing wrong moves in "Monkey Bullet Proof" can be applied to other games or real-life scenarios by providing insights into decision-making and strategy. This can be useful in various fields such as psychology, economics, and artificial intelligence.

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