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Quadratic Functions Projectile Motion

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Quadratic Functions Projectile Motion

Use the given height rules to explore projectile motion. Height is measured in metres and time in seconds. Show working for calculations and round decimal answers to 2 decimal places where needed.

Reading a Projectile Rule

A ball is launched from a platform. Its height is modelled by h = -4t² + 16t + 1, where h is height in metres and t is time in seconds.

1.What type of function is h = -4t² + 16t + 1?

Linear
Quadratic
Cubic
Exponential

2.Use h = -4t² + 16t + 1 to calculate the ball’s height after 1 second.

3.For h = -4t² + 16t + 1, find the ball’s height at t = 2 seconds and at t = 4 seconds.

4.According to h = -4t² + 16t + 1, how does the ball’s height change between 2 seconds and 4 seconds?

It increases
It decreases
It stays constant

Tables and Turning Points

For the next questions, use the height rule h = -2t² + 12t + 3.

Time, t (s)

Height, h (m)

________

5.For h = -2t² + 12t + 3, at what time does the projectile reach its maximum height?

6.For h = -2t² + 12t + 3, state what the y-intercept represents in this situation.

7.For h = -2t² + 12t + 3, give the coordinates of the vertex and explain what it means for the projectile.

8.A second ball follows h = -5t² + 20t + 2. Without finding either maximum exactly, decide whether its maximum height is higher or lower than the maximum for h = -4t² + 16t + 1. Explain using the vertex time and height rule.

Applying the Model

Use algebra and the features of quadratic functions to interpret projectile paths.

9.A cricket ball’s height is modelled by h = -5t² + 20t + 5. Use h = 0 to estimate when the ball reaches the ground. Give the positive time to 2 decimal places.

10.Two projectiles have height rules A: h = -5t² + 20t + 2 and B: h = -5t² + 30t + 2. Which stays in the air longer, and which reaches a greater maximum height? Give a reason for both choices.