Source: High School Physics Olympiad
Problem Sets:
Problem
A truck's canopy covers the cargo area only up to point $A$; a passenger may sit at the rear point $B$. The line $AB$ makes an angle $\varphi = 30°$ with the vertical, and point $C$ lies on the truck bed directly below $A$. The truck drives through rain on a level straight road. When its speed is $u_1 = 6$ km/h, point $C$ is just barely not hit by raindrops; when its speed is $u_2 = 18$ km/h, point $B$ is just barely not hit.
Let the rain have horizontal velocity component $v_x$ (positive in the truck's direction of motion) and downward vertical component $v_y$.
At $u_1 = 6$ km/h, the edge $A$ just shields point $C$ directly below it, so in the truck frame the rain falls vertically:
$$v_x - u_1 = 0 \quad\Rightarrow\quad v_x = 6 \text{ km/h}$$At $u_2 = 18$ km/h, the relative rain velocity is along $AB$, tilted $\varphi = 30°$ backward from the vertical. Its horizontal component is $|v_x - u_2| = 12$ km/h, so:
$$\tan 30° = \frac{12}{v_y} \quad\Rightarrow\quad v_y = 12\sqrt{3} \approx 20.8 \text{ km/h}$$Therefore:
$$v = \sqrt{v_x^2 + v_y^2} = \sqrt{36 + 432} = 6\sqrt{13} \approx 21.6 \text{ km/h} \approx 6.0 \text{ m/s}$$The rain is tilted forward (in the truck's direction of motion) from the vertical by $\arctan\frac{6}{12\sqrt{3}} \approx 16°$.