## Maths Department Help for Local A-Level Students

Testing differential equations with the help of parachutes

Two local Further Mathematics A-Level students visited Lancaster University's Department of Mathematics and Statistics in April for help with their differential equations coursework.

Kevin Crooks (Carr Hill High School, Kirkham) and Keaton Dickinson (Lytham St Annes High School) are both studying through the Lancaster and Cumbria Further Mathematics Network, which is based in the department.

The network allows students to study for Further Mathematics A/AS qualifications even when courses are not offered directly by their school or college.

Kevin and Keaton's differential equations module encourages them to study real-life physical problems, formulate equations which explain the problems and then - hopefully - solve them.

Their coursework problem involves the mathematics of parachutes. A falling parachute is subject to two forces - gravity and air resistance. Can we write down an equation which accurately describes how far the parachute will have fallen after a given period of time? How does the air resistance depend on the speed of the parachute and the size of the canopy?

To try out their theory, Kevin and Keaton made their own parachutes from string, a students' union carrier bag and blu-tac, and threw them down a stairwell from various heights, timing how long they took to reach the ground.

The data from this practical experiment allowed the pair to check the accuracy of their theoretical calculations.

Wed 18 April 2007