I've realised that I don't know what this shape looks like. I will tweet first, make a guess, then do some simulations.

You launch a projectile into the air. If you only know the launch angle and speed roughly, where could it be after T seconds?

My thoughts:

T=0: at the origin.
T→∞: An interval around a point on the ground.
Other T: something like an ellipse, maybe squashed against the ground. I don't think it has to be convex.

I've made a @geogebra worksheet. Point A is the position of the projectile, and B controls the launch angle and speed. I've turned on trace for both.
When B traces a square, A traces a windscreen wiper shape. Makes sense!

Here's the geogebra worksheet: geogebra.org/calculator/gfg…