# Solving the Monkey-Zookeeper Problem: Minimum Velocity Needed

• ziddy83
In summary, the minimum muzzle velocity of the dart must be high enough for it to hit the monkey before reaching the ground. This can be calculated by using the equations y = \frac{1}{2}gt^2 and v = x\sqrt{ \frac{g}{2y} }, where y is the height of the tree, x is the distance between the tree and the zookeeper, and g is the acceleration due to gravity. By finding the amount of time it takes for the monkey to fall and the dart to travel 90 meters, the minimum muzzle velocity can be determined.
ziddy83
Im having issues with this problem...

A zookeeper with a tranqualizer dart gun and a monkey (1.5kg) are both 25 m above the ground in trees 90 m apart. Just as the zookeeper shoots the gun, the monkey drops from the tree. What must the minimum muzzle velocity of the dart have been for it to hit the monkey before reaching the ground?

Im not sure how to start this...so the monkey would be falling at 1/2 gt^2. And at sometime the dart and the monkey will be at the same Y. How would i set up the equations to solve this? Thanks

The higher the muzzle velocity is, the farther the dart will go (horizontally). Which also means that, the higher the muzzle velocity is, the higher the dart will be when it reaches the tree (25 metres away). Keeping that into consideration, where would the dart and monkey be if the dart hit the monkey with the lowest possibly muzzle velocity? Figure that out and you should be well on your way.

The monkey and the dart would probably be right above the ground at the point of contact. So...if the tree is 90 meters high, then i can use -90 as the Y in the height function to find t, and then plug that t into x = [v cos(a)]t, does that seem right?

You're almost there. Now, you need to find a. The question tells you what it is. Pay close attention to the words used. What would it be?

From your book, you should know that the velocity in the x and y are separate.

You solved the first part with knowing the amount of time it takes for the monkey to fall. All you need now is to know the amount of time it takes for a dart to go 90 meters.

What you started out with inquiring was correct:

$$y = \frac{1}{2}gt^2$$

I was semi wrong in stating you did not need this equation, you know that the hunter is shooting straight meaning the angle ($$a$$) is $$0$$.

$$x = vt\cos{a} \rightarrow x = vt\cos{0} \rightarrow x = vt$$

With solving for $$t$$ you get the following:

$$t = \sqrt{ \frac{2y}{g} }$$

In knowing that x and y are separate, you know that the velocity in the x direction is the following:

$$x = vt$$

In combining the two equations you will get

$$v = x\sqrt{ \frac{g}{2y} }$$

Last edited:

## 1. What is the Monkey-Zookeeper Problem?

The Monkey-Zookeeper Problem is a famous problem in computer science that involves a group of monkeys trying to escape from their enclosure while being closely monitored by a zookeeper. The goal is to find the minimum velocity needed for the zookeeper to catch all the monkeys and prevent them from escaping.

## 2. Why is solving the Monkey-Zookeeper Problem important?

The Monkey-Zookeeper Problem is important because it has real-world applications in fields such as robotics, traffic control, and resource allocation. Finding the minimum velocity needed to solve this problem can help optimize these systems and improve efficiency.

## 3. What are some strategies for solving the Monkey-Zookeeper Problem?

Some strategies for solving the Monkey-Zookeeper Problem include using mathematical models and algorithms, such as dynamic programming and greedy algorithms, to find the minimum velocity. Additionally, computer simulations and experiments can also be used to test different scenarios and solutions.

## 4. What are the challenges in solving the Monkey-Zookeeper Problem?

One of the main challenges in solving the Monkey-Zookeeper Problem is that it is a complex optimization problem with many variables and constraints. It also requires considering the behavior and movements of multiple agents (monkeys and the zookeeper) in a dynamic environment. Additionally, finding the exact minimum velocity may be computationally expensive and time-consuming.

## 5. How can the solution to the Monkey-Zookeeper Problem be applied in other fields?

The solution to the Monkey-Zookeeper Problem can be applied in other fields that involve optimizing the movement and interaction of multiple agents, such as in robotics and artificial intelligence. It can also be used in resource management and scheduling problems where efficient allocation and coordination of resources is important.

• Introductory Physics Homework Help
Replies
10
Views
9K
• Introductory Physics Homework Help
Replies
4
Views
4K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
4K
• Introductory Physics Homework Help
Replies
18
Views
4K
• Introductory Physics Homework Help
Replies
7
Views
4K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
8
Views
3K
• Introductory Physics Homework Help
Replies
4
Views
10K