Monkey/Hunter Problem

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Unit: 2D Kinematics

Prerequisites

Projectile Motion

Later Topics

None

Multi-Step Problem Preview

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Part 1

A wildlife conservationist needs to safely capture an escaped monkey that has climbed to the top of a tall tree of height $h$ .

The conservationist stands a distance $d$ away from the base of the tree with a tranquilizer gun that fires darts at $v_0 \text{ m/s}$ . Here's the challenge: the moment the gun fires, the startled monkey will drop from the tree and begin falling under gravity.

In this multi-step problem, we will ultimately determine the angle at which the conservationist must aim to successfully hit the falling monkey.

Naively, the conservationist aims the tranquilizer gun directly at the monkey. Find the general equation that expresses the value of that naive shooting angle.

Correct!

Solution:

The naive aiming angle is along the line of sight from the conservationist to the monkey, forming a right triangle with vertical side $h$ and horizontal side $d$ . Thus,

$\tan(\theta_{naive}) = \frac{h}{d}$ ,

so $\theta_{naive} = \arctan\!\left(\frac{h}{d}\right)$ .

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