# Problem №3 (15 points)

Raindrops fall vertically at a speed of 2 m/s. The mass of one drop is 5 mg. There are 400 drops in one cubic meter of air. How long will it take to completely fill a cylindrical vessel with a height of 20 cm and a base area of 10 cm $^{2}$ with water? The density of water $\rho_{B}=1000 \kappa g / \mathrm{M}^{3}$.

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# Solution:

In one cubic meter of air, there is $400 \cdot 5 \cdot 10^{-6}=0.002$ kg of water.

That is, 0.004 kg of water falls on one square meter of surface in one second (3 points).

Therefore, on 10 cm$^2$, 0.004 kg of water falls in one second, which is $4 \cdot 10^{-6}$ kg of water.

A fully filled container will contain:

$m=\rho V=1000 \cdot 0.2 \cdot 10 \cdot 10^{-4}=0.2$ kg of water.

That is, the container will be filled in:

$t=\frac{0.2}{4 \cdot 10^{-6}}=5 \cdot 10^{4}$ seconds $\Rightarrow \approx 833.3$ minutes $\approx 13.9$ hours.