Water level is maintained in a cylindrical vessel up to a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel (figure 13-E11)?

Question

Philoid · Accepted Answer

The height of the vessel is H. Let the height of the hole be h.

The height of water above the hole is H-h.

therefore, the velocity with which water exits is

Let the time of flight be t

The horizontal distance travelled is

Now we need to maximize this function.

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