Throw off a Cliff

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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 .

Contributed by: Antoine Weis (March 2011)
Additional contributions by: Fernand Brunschwig
Open content licensed under CC BY-NC-SA



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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