How to Model the Movement of Projectiles

Let’s solve a problem using some of the beautiful equations that model projectile motion

A projectile is a particle or body that is thrown into the air, usually at an angle to the horizontal. Think shot put or javelin in athletics. The mathematics for modeling projectile motion is beautiful and relatively simple, and is a core part of high school mathematics teaching in mechanics and applied mathematics.

In this article I am going to solve an interesting problem regarding a projectile. I will use this problem to illustrate the mathematics for those of you who don’t know it, and we will also see how we can use the mathematics to show that certain types of flight paths of projectiles are possible or not possible. My thanks to Archie Smith who drew my attention to this problem, which was taken from a recent Cambridge Sixth Term Examination Paper (STEP). I’ve adjusted the question a little to make it more interesting.

First let’s lay out the problem:

Two thin walls of height 2a lie a distance of a apart from each other, where a is an arbitrary positive value. On a calm day with no air resistance, a particle A is projected from the ground in the direction of the walls and in a path perpendicular to the walls. The particle has initial speed of…