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Water leaks out of a small hole in the side of a bucket. The hole is...

Water leaks out of a small hole in the side of a bucket. The hole is a distance d below the surface of the water, and the diameter of the hole is much smaller than the diameter of the bucket. Principles Example 18.9 derived an expression for the speed v2 at which water exits the hole by assuming that v1 ≈ 0 for the speed at which the water surface moves downward.

Derive an expression for v2 when v1 cannot be ignored.

Answer in terms of d, v1, and g.

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