What are the equations to describe the physics of a falling leaf?
Depends what he or she meant by fully. The first equation would be working out how long it takes to reach the ground, and how fast it’s going when it arrives. This is actually going to be a differential equation since the air resistance on the leaf will cause it to reach terminal velocity very quickly, and will have the form: F = mg – k(dx^2/dt^2). Terminal velocity will be reached when the net force is zero, i.e. the leaf is not accelerating but falling at a steady speed. Secondly, you may want to consider how the leaf rotates. This would call for an angular momentum equation. I can’t think why it would be useful to do this, but you could come up with an equation describing the leaf’s rotation by considering the position of its centre of mass. If the leaf was a ball, this would be trivial. The leaf isn’t the same shape all over and the equation gets a bit harder, involving integral calculus. However, this may have been what your teacher was getting at. It’s unlikely the leaf continues
