Raindrops

The car runs on a horizontal track at a constant speed of 20 m²-1. It is raining. Raindrops fall in a vertical direction at a speed of 6 m/s.
a) How fast is the speed of the drops relative to the car windows?
b) What is the angle of the raindrops on the car window with the vertical direction?

Correct answer:

v =  20.8806 m/s
α =  73.3008 °

Step-by-step explanation:

$$\begin{gathered} v_1=20\text{m/s} \\ {v}_2=6\text{m/s} \\ {v}^2=v_1^2+v_2^2 \\ v=\sqrt{v_1^2+v_2^2}=\sqrt{20^2+6^2}=2\sqrt{109}=20.8806\text{m/s} \end{gathered}$$

$$\begin{gathered} \tan \alpha =v_1:v_2=20:6=\frac{10}{3}\doteq 3.3333=10:3 \\ \alpha =\frac{180°}{\pi }\cdot \arctan (v_1/v_2)=\frac{180°}{\pi }\cdot \arctan (20/6)=73.3008^{\circ }=73°18^{\prime }3" \end{gathered}$$

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