7 A water tank of height 1 m has a square base 2 m x 2 m. When a tap at its base is opened, the water flows out at a rate proportional to the square root of the depth of the water at any given time. Suppose the depth of the water is h m, and V is the volume of water remaining in the tank after t minutes. a Write down a differential equation involving dV and h to model this situation. dt b Explain why V = 4h m3 at time t, then use the chain rule to write down a differential equation involving dh and h only. dt C The tank is initially full. When the tap is opened, the water level drops by 19 cm in 2 minutes Findd the t kes for the tonk to em

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.