Rain is falling vertically down on a car moving at 11 m/s. Tracks made by the raindrops on the...

Question:

Rain is falling vertically down on a car moving at 11 m/s. Tracks made by the raindrops on the side window of the car are inclined 55 degrees with the vertical. Find the speed of the raindrop relative to the ground.

vector addition

In this problem, we are asked to determine the velocity of the rain on the side window of a moving car with respect to the ground given the vertical velocity of the rain. The inclined path of the rain is due to vertical velocity of the rain and the horizontal velocity of the car. The angle of inclination of the path is determined using the following equation: {eq}\cos\theta=\frac{v_y}{v}{/eq}

Answer and Explanation:

Given:

vertical velocity of the rain = {eq}v_y=11\ m/s{/eq}

angle of the rain on the window of the car = {eq}\theta=55^\circ{/eq}

The speed of the rain on the window of the car with respect to the ground (v) is obtained using the following relation:

$$\cos\theta=\frac{v_y}{v}$$

Solving for v:

$$v=\frac{v_y}{\cos\theta}=\frac{11\ m/s}{\cos {55^\circ}}=19.18\ m/s$$


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