Water flows from the base of rectangular tank, of depth 16 meters. The rate of flow of the water is proportional to the square root of depth at any time $\mathrm{t}$. If depth is $4 \mathrm{~m}$ when $\mathrm{t}=2$ hours, then after 3.5 hours the depth (in meters) is

Question

Aicharya · Accepted Answer

Given that $\frac{\mathrm{d} x}{\mathrm{dt}} \propto \sqrt{x}$ $	herefore \quad \frac{\mathrm{d} x}{\mathrm{dt}}=\mathrm{a} \sqrt{x}$, for real number a $	herefore \quad \int \frac{\mathrm{d} x}{\sqrt{x}}=\int \mathrm{adt}$ $	herefore \quad 2 \sqrt{x}=\mathrm{at}+\mathrm{c}$ When $\mathrm{t}=0, x=16$ $	herefore \quad$ (i) $\Rightarrow \mathrm{c}=8$ $	herefore \quad$ (i) becomes $2 \sqrt{x}=$ at +8 When $\mathrm{t}=2, x=4$ $	herefore \quad$ (ii) $\Rightarrow \mathrm{a}=-2$ $	herefore \quad$ (ii) becomes $2 \sqrt{x}=-2 t+8$ $	herefore \quad$ when $\mathrm{t}=3.5$ (iii) $\Rightarrow x=0.25 \mathrm{~m}$

Water flows from the base of rectangular tank, of depth 16 meters. The rate of flow of the water is…

Solution