A certain liquid flows out from a vertical pipe has a definite shape.$$ The liquid is in free fall once it is out of the pipe.$$ The moment the liquid leaves the pipe the stream has a radius r$0$ and speed v$0=1\mathrm{.}20$ meter$/$sec$.$

An equation for the radius of the stream as a function of vertical distance y is the following

r$=$r$0(($v$0)2($v$0)2+2$gy$)14$

a$)$ What is the radius of the stream as a function of time t$?$

That is$,$ what is r$($t$)?$

b$)$ How fast is the stream falling at r$=$r$02?$

That is$,$ what is the speed of the stream when the radius of the stream is $1/2$ its initial radius with initial speed of stream v$0=1\mathrm{.}20$ m$/$sec$?$