Quadratic Functions Projectile Motion

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🎯 Part 1: Understanding Projectile Motion

1. A football is kicked into the air. Its height (in metres) above ground is given by the formula: h = -5t² + 20t + 2, where t is time in seconds. Which of these describes this type of function?

Linear function

Quadratic function

Cubic function

Exponential function

2. Using the formula h = -5t² + 20t + 2, calculate the height of the football at t = 1 second.

Height = ________ metres

3. Calculate the height at t = 2 seconds and t = 3 seconds.

At t = 2 seconds: Height = ________ metres

At t = 3 seconds: Height = ________ metres

4. What happens to the height values as time increases from t = 2 to t = 3 seconds?

The height increases

The height decreases

The height stays the same

📊 Part 2: Analysing Quadratic Graphs

5. Complete this table for the projectile motion formula h = -5t² + 20t + 2:

t = 0: h = ________ metres

t = 1: h = ________ metres (already calculated above)

t = 2: h = ________ metres (already calculated above)

t = 4: h = ________ metres

6. Based on your calculations, at what time does the football reach its maximum height?

Maximum height occurs at t = ________ seconds

7. In the context of projectile motion, what do these key features represent?

a) The y-intercept (when t = 0): _________________________________

b) The vertex (highest point): ___________________________________

8. A basketball player shoots a ball with the height formula h = -4.9t² + 15t + 2.1. Without calculating, predict whether this ball will reach a higher or lower maximum height than the football. Explain your reasoning.

🚀 Part 3: Real-World Applications

9. A cricket ball is hit with height formula h = -5t² + 25t + 1. Use your calculator or graphing software to find when the ball hits the ground (h = 0).

The ball hits the ground at t = ________ seconds

10. Extension Challenge: Compare two projectiles:

Projectile A: h = -5t² + 20t + 2

Projectile B: h = -5t² + 30t + 2

Without graphing, predict which projectile will:

a) Stay in the air longer: Projectile ________

b) Reach a greater maximum height: Projectile ________

c) Explain your reasoning: