Question

A car travels due east with a speed of 40.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 64.0° with the vertical. Find the velocity of the rain with respect to the car and the earth. (Enter the magnitude of the velocity.)

Answer 1

Answer:

The velocity of rain with respect to earth is 23.1 km/h.

Explanation:

Let

$\overrightarrow{V_r}$ be the velocity of rain with respect to ground

$\overrightarrow{V_c}=40\widehat{i}$ be the velocity of car with respect to ground

It is given that

$\overrightarrow{V_c}=40\widehat{i}$

Now the velocity of rain with respect to car is given by

$\overrightarrow{V_{rc}}=\overrightarrow{V_r}-\overrightarrow{V_c}\\\\\overrightarrow{V_{rc}}=-V_r\widehat{j}-40\widehat{i}$ since the rain is falling vertically downwards

Thus the relative angle of the rain made with vertical  with respect to car is given by

$\theta =tan^{-1}(\frac{|V_{x}|}{|V_y|})\\\\|\frac{v_x}{v_y}|=tan(\theta )$

Applying values we get

$tan(60)=\frac{40}{v_{y}}\\\\\therefore v_y=\frac{40}{tan(60)}=23.1km/h$