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A water tank of height h has a small hole at height y. The water is replenished to keep h from changing. The water squirting from the hole has range x. The range approaches zero as y → 0, because the water squirts right onto the ground. The range also approaches zero as y→ h, because the horizontal velocity becomes zero. Thus there must be some height y between 0 and h for which the range is a maximum. (1) Find an algebraic expression for the flow speed v for which the water exits the hole at height y. (2) Find an algebraic expression for the range of a particle shot horizontally from height h with speed v. (3) Combine your expressions from parts (1) and (2). Then find the maximum range max and the height y of the hole.

A water tank of height h has a small hole at height y. The water is replenished to keep h from changing. The water squirting from the hole has range x. The range approaches zero as y → 0, because the water squirts right onto the ground. The range also approaches zero as y→ h, because the horizontal velocity becomes zero. Thus there must be some height y between 0 and h for which the range is a maximum. (1) Find an algebraic expression for the flow speed v for which the water exits the hole at height y. (2) Find an algebraic expression for the range of a particle shot horizontally from height h with speed v. (3) Combine your expressions from parts (1) and (2). Then find the maximum range max and the height y of the hole.

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A water tank of height h has a small hole at height y. The water is replenished to keep h from changing. The water squirting from the hole has range x. The range approaches zero as y → 0, because the water squirts right onto the ground. The range also approaches zero as y→ h, because the horizontal velocity becomes zero. Thus there must be some height y between 0 and h for which the range is a maximum. (1) Find an algebraic expression for the flow speed v for which the water exits the hole at height y. (2) Find an algebraic expression for the range of a particle shot horizontally from height h with speed v. (3) Combine your expressions from parts (1) and (2). Then find the maximum range max and the height y of the hole.
Transcribed Image Text:A water tank of height h has a small hole at height y. The water is replenished to keep h from changing. The water squirting from the hole has range x. The range approaches zero as y → 0, because the water squirts right onto the ground. The range also approaches zero as y→ h, because the horizontal velocity becomes zero. Thus there must be some height y between 0 and h for which the range is a maximum. (1) Find an algebraic expression for the flow speed v for which the water exits the hole at height y. (2) Find an algebraic expression for the range of a particle shot horizontally from height h with speed v. (3) Combine your expressions from parts (1) and (2). Then find the maximum range max and the height y of the hole.
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