Consider a column of water as it falls from a faucet. The opening in the faucet has radius r0 and the water comes out with initial velocity v0. Define y to be the distance below the faucet. As the water falls (y increases), it accelerates due to gravity and the stream narrows. a) Assuming streamline flow, find an expression for the velocity of the water for any distance below the faucet. b) The stream obeys the continuity equation. Use this to determine the radius of the stream as a function of y. c) At what distance y1/2 will the radius of the stream be half its original radius? At what distance y1/3 will it be a third? d)Comparey1/2 andy1/3 forv0 =1m/sandv0 =0.1m/s(useg=10m/s2).