Throw off a Cliff

Two-dimensional display of the trajectory of an object thrown from a cliff into the sea. Parameters of the trajectory that you can vary are the cliff height , the initial velocity , and the initial angle .


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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
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