Question

Snow is falling vertically at a constant speed of $8.0\text{m/s}$. At what angle from the vertical do the snowflakes appear to be falling as viewed by the driver of a car traveling on a straight level road with a speed of $8\sqrt{3}\text{m/s}$?

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${75}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

Given,
Speed of snow falling, $V_s=8.0\text{m/s}$
Speed of car, $V_c=8\sqrt{3}\text{m/s}$

Let us assume, $V_n=$ velocity of snowflakes as seen by driver, makes $\theta$ angle with vertical.

From figure,
$\text{tan}\theta =\frac{|-V_c|}{|V_s|}$
$\Rightarrow \text{tan}\theta =\frac{8\sqrt{3}}{8.0}$
$\Rightarrow \text{tan}\theta =\sqrt{3}$
$\Rightarrow \theta ={60}^{\circ }$
So, snowflakes make an angle of ${60}^{\circ }$ with vertical as seen by the driver of car.