(a)[4]
Show that $\frac{dh}{dt}=\frac{500-h^2}{250}$.
(b)[5]
Knowing that $h=0$ when $t=0$, determine the time needed for the water depth in the tank to rise to $20\text{ cm}$.
Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
The diagram depicts a tank used to store water. It has the form of a cube with side $50\text{ cm}$. At time $t$ seconds, the water depth in the tank is $h\text{ cm}$. Water is fed into the tank at $5000\text{ cm}^3\text{ s}^{-1}$. Water leaves the tank through a hole in the base at a rate proportional to $h^2$. When $h=20$, the water depth is rising at $0.4\text{ cm s}^{-1}$.