Veterinarian and Monkey Problem

Projectile motion: the tranquilizer dart and monkey fall with the same acceleration g.

Controls

Rifle Angle

Slider angle = 60.0°

Bullet speed = 40 m/s
Monkey height = 63.5 m
Horizontal distance = 80 m

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Check Answer

Student name:

Enter aiming angle (1 decimal place):

Hunter and Monkey Projectile Motion Simulation

This interactive 3D physics simulation demonstrates the classic The Veterinarian and Monkey problem. A tranquilizer dart is fired at a monkey at the same instant the monkey begins to fall. The simulation shows why the tranquilizer dart hits the monkey when the rifle is aimed directly at the monkey’s initial position.

Physics Principle

The key idea is that both the tranquilizer dart and the monkey experience the same downward gravitational acceleration. Gravity causes both objects to fall by the same vertical distance during the same time interval.

y = y₀ + v₀y t - ½gt²

Because the tranquilizer dart and monkey both have the same gravitational term, the downward displacement caused by gravity cancels when comparing their relative vertical motion.

What Students Learn

Projectile motion has independent horizontal and vertical components.
Gravity affects both the tranquilizer dart and the monkey equally.
The rifle should be aimed directly at the monkey’s initial position.
The required bullet speed must be large enough to reach the monkey before it hits the ground.

Classroom Questions

Would the answer change if the monkey were bigger or smaller?
Would the answer change if the tranquilizer dart speed changed?
What is the minimum bullet speed needed before the monkey reaches the ground?