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?"
Prerequisite Connection
You can write parametric equations and evaluate trigonometric functions.
Today's Increment
We model projectiles with parametric equations, finding max height, range, and time of flight.
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
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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