Water is running out of a faucet, falling straight down,
withan initial speed of 0.35 m/s. at whatdistance below the faucet
is the radius of the stream reduced toone-half its value at the
faucet?

To solve this problem we will apply the concepts related to the continuity equations. Here we will relate the input flow and the output flow depending on the cross-sectional area and the fluid velocity.

When we find the speed found, apply the kinematic equations of motion that relate the change in speed with acceleration (gravity) and distance traveled. So:

Here,

= Cross sectional Area at each section

= Velocity at each section

For a circle we have that the relation would be,

With the previous relation given as

We have replacing that,

From the cinematic equations of motion we have to

Therefore the distance will be 9.37cm