# Kinematics in Two Dimensions (Monkey and Hunter Thought Experiment)

• griffin_neal
In summary, the conversation is about a question that involves setting up a reference frame and writing equations of motion for a monkey and a tennis ball. The person is struggling to understand the question and is asked to explain which part they are having trouble with.
griffin_neal
Poster warned for not providing an attempt at a solution
Homework Statement
This week, I was assigned this assignment, which is really giving me a tough time. It involves the classic monkey and hunter thought experiment. I am at a total loss at how to even approach this question. Here is what the question asks:

"
The monkey and hunter is a thought experiment to illustrate the independence of the horizontal and vertical motion of a projectile.
A student models the experiment by projecting a table tennis ball horizontally at a toy monkey.
The ball and monkey are initially at the same height, H, above the bench. The monkey drops the instant the ball is projected.
The monkey and the ball will always meet, irrespective of their horizontal separation.

a) Set up a reference frame that you find useful and write the equations of motion for the monkey
and the tennis ball.
b) From the equations of motion, please find the equations for the trajectory of the tennis ball and the monkey.
c) Show, mathematically, that for any value of velocity of the tennis ball, it will always strike the
monkey (ignore the table counter)
d) Show, mathematically, that for any horizontal separation, the tennis ball will always strike the
monkey (ignore the table counter). You can use your results from the previous question.
e) Show that the time taken to fall to the bench is the same for both the monkey and the tennis ball.
f) If we do not ignore the counter, what must the relationship between the initial velocity of the
tennis ball and the separation between them be in order that the two meet while still in flight?
g) What must not be changed in the system's design to ensure the results of the thought
experiment remain valid?
"
Relevant Equations
All SUVAT equations of motion:

s = ([u + v]t)/2
v = u + at
s = ut + 1/2at^2
v2 =u^2 + 2as

griffin_neal said:
I am at a total loss at how to even approach this question.
That won't do. Per forum rules, you must show some attempt.
There are many parts. You must at least have some thoughts on some of them.

griffin_neal said:
I am at a total loss at how to even approach this question. Here is what the question asks:
The statement of the problem kindly provides a thoughtful and detailed step-by-step procedure of the method to follow in order to answer the question. You claim you are "at a total loss" (emphasis mine). Let's begin at the beginning, step (a). What part of "Set up a reference frame that you find useful and write the equations of motion for the monkey and the tennis ball" can't you understand?

topsquark, Lnewqban and DrClaude
Use a the ground as a reference frame. Assume the ground is stationary and that the monkey moves with respect to it.

## 1. How does the monkey's initial velocity affect the outcome of the thought experiment?

The monkey's initial velocity plays a crucial role in determining whether it will successfully avoid the hunter's bullet. If the monkey's initial velocity is greater than the bullet's, it will be able to reach the tree before the bullet reaches it. However, if the monkey's initial velocity is less than the bullet's, it will be hit by the bullet.

## 2. What is the significance of the angle at which the hunter shoots the bullet?

The angle at which the hunter shoots the bullet determines the horizontal and vertical components of the bullet's velocity. This, in turn, affects the trajectory of the bullet and its ability to hit the monkey. If the angle is too high or too low, the bullet may miss the monkey altogether.

## 3. How does the distance between the monkey and the tree impact the outcome of the thought experiment?

The distance between the monkey and the tree is a crucial factor in determining whether the monkey will be able to successfully reach the tree before the bullet reaches it. The closer the monkey is to the tree, the higher its chances of avoiding the bullet. However, if the distance is too great, the monkey may not be able to reach the tree in time.

## 4. Can the thought experiment be applied to real-life scenarios?

While the monkey and hunter thought experiment is a simplified scenario, the principles of kinematics in two dimensions can be applied to real-life situations. For example, it can be used to calculate the trajectory of a projectile, such as a ball being thrown or a rocket being launched.

## 5. How does air resistance affect the outcome of the thought experiment?

In the thought experiment, air resistance is assumed to be negligible. However, in real-life scenarios, air resistance can significantly impact the trajectory of a projectile. It can cause the projectile to slow down and deviate from its expected path, making it more difficult to predict the outcome of the scenario.

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