Lesson 16.3

Parametric Modeling of Projectile Motion

Using equations to find the maximum height and range of an object.

Introduction

When you throw a ball, kick a soccer goal, or launch a rocket, the object follows a curved path through the air.Projectile motion is the perfect application of parametric equations: the horizontal position and vertical position are both functions of time, allowing us to answer questions like "How high does it go?" and "Where does it land?"

1

Prerequisite Connection

You can write parametric equations and evaluate trigonometric functions.

2

Today's Increment

We model projectiles with parametric equations, finding max height, range, and time of flight.

3

Why This Matters

Projectile motion applies to sports, engineering, and physics simulations.

Projectile Equations

Parametric Equations (no air resistance)

Maximum Height

Range (from h₀ = 0)

Interactive: Adjust Launch Parameters

Max Height ≈ 63.8 mRange ≈ 255.1 m

Worked Examples

Example 1: Finding Max Height

A ball is launched at 30 m/s at 60°. Find max height (g = 9.8).

Example 2: Finding Range

Same ball. Find the range.

Example 3: Time of Flight

Find total flight time.

Common Pitfalls

Degrees vs radians - Match your calculator mode to your angle!

Wrong g value - Use 9.8 m/s² or 32 ft/s² consistently.

Real-World Application

Sports Analytics

Baseball, golf, and basketball all use projectile motion to analyze optimal launch angles and speeds.

Practice Quiz

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