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21 December, 13:08

A car travels due east with a speed of 38.0 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 72.0° with the vertical. Find the velocity of the rain with respect to the following reference frames. (Enter the magnitude of the velocity.)

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  1. 21 December, 13:36
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    Answer: 116.926 km/h

    Explanation:

    To solve this we need to analise the relation between the car and the Raindrops. The cars moves on the horizontal plane with a constant velocity.

    Car's Velocity (Vc) = 38 km/h

    The rain is falling perpedincular to the horizontal on the Y-axis. We dont know the velocity.

    However, the rain's traces on the side windows makes an angle of 72.0° degrees. ∅ = 72°

    There is a relation between this angle and the two velocities. If the car was on rest, we will see that the angle is equal to 90° because the rain is falling perpendicular. In the other end, a static object next to a moving car shows a horizontal trace, so we can use a trigonometric relation on this case.

    The following equation can be use to relate the angle and the two vectors.

    Tangent (∅) = Opposite (o) / adjacent (a)

    Where the Opposite will be the Rain's Vector that define its velocity and the adjacent will be the Car's Velocity Vector.

    Tan (72°) = Rain's Velocity / Car's Velocity

    We can searching for the Rain's Velocity

    Tan (72°) * Vc = Rain's Velocity

    Rain's Velocity = 116.926 km/h
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