   Chapter 3, Problem 22P

Chapter
Section
Textbook Problem

A car travels due east with a speed of 50.0 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 60.0° with the vertical. Find the velocity of the rain with respect to (a) the car and (b) the Earth.

(a)

To determine
The velocity of the rain with respect to the car.

Explanation

Let the eastward direction be the positive x axis and the upward direction is vertically upward.

The velocity of the car relative to the Earth is,

vCE=50.0km/h in the +x -direction

The velocity of the rain with respect to the Earth is,

vRE=vrain in the y -direction

The relation between the relative velocities are,

vRE=vCE+vRC

Thus, the relative velocity vectors form a 90.0° vector triangle.

Now, the velocity of the rain can be found from the relation tanθ=vCEvRE .

vrain=vCEtanθ

Substitute 50.0km/h for vCE and 60

(b)

To determine
The velocity of the rain with respect to the Earth.

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