A water tank of height h has a small hole at height y. The water is replenished to keep h fromchanging. 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, becausethe horizontal velocity becomes zero. Thus there must be some height y between 0 and h for whichthe range is a maximum.(1) Find an algebraic expression for the flow speed v for which the water exits the hole at heighty.(2) Find an algebraic expression for the range of a particle shot horizontally from height h withspeed v.(3) Combine your expressions from parts (1) and (2). Then find the maximum range max andthe height y of the hole.

Barnaulli equation:P1+ρgh1+12ρv12=P2+ρgh2+12ρv22Where, P1 is the atmosphere pressure at height hP2…

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