This carries on our exploration of projectile motion – this time we will explore what happens if gravity is not fixed, but is instead a function of time. (This idea was suggested by and worked through by fellow IB teachers Daniel Hwang and Ferenc Beleznay). In our universe we have a gravitational constant – […]

Projectile Motion III: Varying gravity We can also do some interesting things with projectile motion if we vary the gravitational pull when we look at projectile motion. The following graphs are all plotted in parametric form. Here t is the parameter, v is the initial velocity which we will keep constant, theta is the angle […]

Projectile Motion Investigation II Another example for investigating projectile motion has been provided by fellow IB teacher Ferenc Beleznay. Here we fix the velocity and then vary the angle, then to plot the maximum points of the parabolas. He has created a Geogebra app to show this (shown above). The locus of these maximum points […]

Envelope of projectile motion For any given launch angle and for a fixed initial velocity we will get projectile motion. In the graph above I have changed the launch angle to generate different quadratics. The black dotted line is then called the envelope of all these lines, and is the boundary line formed when I […]

Classical Geometry Puzzle: Finding the Radius This is another look at a puzzle from Mind Your Decisions. The problem is to find the radius of the following circle: We are told that line AD and BC are perpendicular and the lengths of some parts of chords, but not much more! First I’ll look at my […]

Further investigation of the Mordell Equation This post carries on from the previous post on the Mordell Equation – so make sure you read that one first – otherwise this may not make much sense. The man pictured above (cite: Wikipedia) is Louis Mordell who studied the equations we are looking at today (and which […]