Question

Water is running out of a faucet, falling straight down, with an initial speed of 0.50 m/s. At what distance below the faucet is the radius of the stream reduced to one-half its value at the faucet?
That will happen when the velocity of the water has increased by a factor of 4.

(stream Area)*(velocity) = constant.

Use conservation of energy to get that distance.

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