Parabola trajectory
A body has the initial velocity v₀ and an angle α to the horizontal line and is moving in the gravity field (of the earth or another planet). The instantaneous velocity v = (vx,vy) at the time moment t can be expressed with the following equations:

where g represents Earth's gravitational constant, x is long distance and y is height distance.

The distances x and y are time-dependend and their equations are:

We've got a constant velocity in the horizontal direction and a constant accelerated velocity in the vertical direction. This describes a parabola, the formula we will get expressing t in both equations explicitely

I f we take in consideration, that the initial height is not the ground level, but the level of the center of gravitiy of the body h₀ than the formula changes to

From this formula we can get the maximal width and the maximal heigth of the jump with ground level zero

Agian in the case, taht we take in consideration the different level for the point of jumping and landing, we get