Shape made by the farthest points on a ramp
A frictionless ramp makes an angle \(a\) to the horizontal, and that angle is adjustable between 0° and 90°.
You slide a mass up the ramp many times, giving it the same initial velocity each time, but setting the ramp to a different angle each time. You note the coordinates of the mass (in the 2D plane of the ramp) each time it reaches its farthest point along the ramp before sliding back down.
If you plot the coordinates you noted for each the trials together on a 2D plane, what shape will those points describe?