How to get to the formula

A vertical cylinder cylinder from the section area taken back 'A1' is open to its top and contains water with depth 'h0'. A hole of area 'A2' is drilled in the bottom (A1> A2).

(A)Show in detail how to get to the formula below with the information data.

h(t)= ( (√h0)-(A2/A1).(√g/√2).t)²

(B)How long does it take to empty the tank after the hole is opened? (The answer must be in functions A1, A2, h0 and g)

Sample Solution