Monkey and the Hunter: Why it Works

The Monkey and The Hunter

Intro:

The widely known story usually tells of a monkey up in a tree who is trying to outsmart a hunter. The hunter takes his time and lines up his shot directly at the monkey. The monkey, who has probably not taken a physics course, thinks that if it drops from the branch as it hears the gunshot (ignoring the sound of speed), the bullet will go over its head. Unfortunately, the monkey does not outsmart the hunter, as the hunter knows of something called gravity. 

We set up this scenario in class using a circuit and a magnet which would release the monkey as the flow of electricity was cut off by the "bullet". We aimed the projectile launcher directly at the monkey and observed that the bullet and monkey collided. But why did this happen? Why didn't the bullet go over the monkey?

What are we trying to show?

This experiment is used to emphasize that the x and y components of an object moving as a projectile are independent of each other. By aiming directly at the monkey rather than above or below, it is evident that gravity (a constant of 9.8 m/s^2) is acting on each object, causing them to fall at the same rate and eventually to collide, regardless of the velocity or x-component of the bullet.

Demo of Experiment

Note: In this demo, the laser confirms that aim is being taken directly at the monkey. Also, notice that the shot is taken with projectiles of various initial velocities. The only resulting difference is the height at which the bullet collides with the monkey.

Why this works:

If the bullet's height (deltaYb) is set equal to the height of the tree (h) minus the distance the monkey falls (deltaYm), we can then prove that aim should be taken at the monkey by finding tan(x) = h/d.

Setup:

Using Kinematics Equations,

deltaYm is given by: -g/2 * t^2   and

delta Yb is given by: vsin(x)t - [g/2 * t^2]

Therefore,

h - [g/2 * t^2] = vsin(x)t - [g/2 * t^2]

h = vsin(x)t

We also know that,

d = vcos(x)t

Since we want to demonstrate that tan(x) = h/d, we should divide the top equation by the second:

h = vsin(x)t

d = vcos(x)t

Velocity and time cancel, and sin(x)/cos(x) can be condensed to tan(x) giving us: tan(x) = h/d, proving that if aim is taken directly at the monkey, the two objects will eventually collide.

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Sources:

“Resource Lesson: Monkey and the Hunter.” PhysicsLAB, Catharine H. Colwell, dev.physicslab.org/Document.aspx?doctype=3&filename=Freefall_monkey.xml.

“Shoot the Monkey.” Youtube, Harvard Natural Sciences Lecture Demonstrations, 22 Aug. 2013, youtu.be/0jGZnMf3rPo.

“The Monkey and Zookeeper.” The Physics Classroom, The Physics Classroom, www.physicsclassroom.com/mmedia/vectors/mzf.cfm.

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