19. As shown in Figure 1, a 

small boat is traveling northward at a speed of $10 \mathrm{~m} / \mathrm{s}$ over the lake, and on a bridge $20 \mathrm{~m}$ above the lake, a car is moving eastward at a speed of $20 \mathrm{~m} / \mathrm{s}$. Currently, the boat is $40 \mathrm{~m}$ south of point $P$ on the water, and the car is $30 \mathrm{~m}$ west of point $Q$ on the bridge (where $P Q \perp$ the water surface). The shortest distance between the boat and the car is $\qquad$ $\mathrm{m}$ (ignoring the sizes of the car and the boat).
19.30.

Assuming after $t \mathrm{~s}$, the distance between the boat and the car is $y \mathrm{~m}$, then
$$
\begin{array}{l}
y=\sqrt{(40-10 t)^{2}+(-30+20 t)^{2}+400} \\
=\sqrt{500(t-2)^{2}+900} \text {. } \\
\end{array}
$$

When $t=2 \mathrm{~s}$, $y$ has a minimum value of $30 \mathrm{~m}$.