Objectives
Students formulate algebraic and trigonometric expressions related to two different sporting arenas and use calculus to establish the ultimate location to kick for goals based on the circumstances provided.
Vocabulary
- Ellipse
- ArcTan
- Derivative
- Solve
About the Lesson
Students start by modelling shots on goal in soccer. The rectangular field shape combined with the specific shooting locations simplifies the mathematics. Once students have finished looking at soccer, they move onto the real situation one AFL player created after taking a mark near the point post. The player walked back along the boundary line, almost all the way to the 50m arc and proceeded to kick a goal! Was this the best place to kick a goal? Use differential calculus, arcTan and coordinate geometry to explore this practical problem.