Tennis Training Wall
A tennis practice wall is angled so the ball rebounds back towards the player instead of straight back. Find the angle that returns the ball exactly the way it came, and design a wall shape that works from any hitting position.
Introduction
A single flat practice wall bounces every ball off at a mirror angle: angle in equals angle out. Some practice walls are tilted from vertical, or built with a step, precisely so that a ball hit straight at them returns straight back to the player rather than to the side. This exploration works out what wall angle achieves that for a given hitting position, then asks a harder question: is there a wall shape that returns every shot to the same fixed point, no matter where the player is standing? This is the same reflective property used by satellite dishes and headlight reflectors, applied in two dimensions instead of three.
Guiding Questions
- A practice wall returns the ball to the player. What angle should the wall make for the ball to come straight back?
- Trace the path of a ball hitting the angled wall using the reflection rule.
- For a player standing in different spots, where should they aim?
- Design a wall shape that returns every shot to a fixed point. Which curve does that, and why?