A water tank of height h has a small hole at height y. Thewater is replenished t

Question

A water tank of height h has a small hole at height y. Thewater is replenished to keep h from changing. The water squirtingfrom the hole has range x. The range approaches zero as y-->0because the water squirts right onto the table. The range alsoapproaches zero as y->h because the horizontal velocity becomeszero. Thus there must be some height y between 0 and h for whichthe range is a maximum
Find an algebraic expression for the flow speed v with whichthe water exits the hole at height y .


Find an algebraic expression for the range of a particle shothorizontally from height y with speed v.

Combine your expressions from parts A and B. Find the maximum rangex (max).

Find the height y of the hole. "Real" water won't achieve quitethis range because of viscosity, but it will be close. A water tank of height h has a small hole at height y. Thewater is replenished to keep h from changing. The water squirtingfrom the hole has range x. The range approaches zero as y-->0because the water squirts right onto the table. The range alsoapproaches zero as y->h because the horizontal velocity becomeszero. Thus there must be some height y between 0 and h for whichthe range is a maximum
Find an algebraic expression for the flow speed v with whichthe water exits the hole at height y .


Find an algebraic expression for the range of a particle shothorizontally from height y with speed v.

Combine your expressions from parts A and B. Find the maximum rangex (max).

Find the height y of the hole. "Real" water won't achieve quitethis range because of viscosity, but it will be close.

Explanation / Answer

a) v = sqrt[2g (h-y)]
b) x = v* sqrt (2y/g)
c) y = 1/2 h for max range, i think you can solve for therest

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