Throw off a Cliff

The trajectory of the object is given by

.

For simplicity, set .

The main goal of the Demonstration is to explore the range of the trajectory, that is, the maximum coordinate that can be achieved with a given height and a given velocity . It is well-known that in the case of a ground-to-ground throw () the range is maximized for , as shown by the snapshots. For this condition no longer holds and the general expression for the range is given by

,

for which the maximal range becomes

.