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A car travels due east with a speed of 50.0 $\mathrm{km} / \mathrm{h}$. Raindrops are falling at a constant speed vertically with respect to the Farth. The traces of the rain on the side windows of the car make an angle of $60.0^{\circ}$ with the vertical. Find the velocity of the rain with respect to (a) the car and (b) the Earth.

(a) $V _ { \mathrm { RC } } = 50 \mathrm { km } \mathrm { h } ^ { - 1 } \mathrm { i } - 28.87 \mathrm { km } \mathrm { h } ^ { - 1 } \mathrm { j }$

(b) The velocity of the rain relative to the Earth is $V _ { \mathrm { RE } } = - 28.87 \mathrm { km } \mathrm { h } ^ { - 1 } \mathrm { j }$

is in -ve y-direction.

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Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

University of Sheffield

so we can, Um imagine this and we can know that the velocity of the car is going to be equal in the velocity of the rain. Relative to the car times sign of Fada. If we can say that here, redraw small diagram. This would be the velocity of the negative velocity of the car. This would be the velocity of the car here. This would be our angle fatal here. And this would be the velocity of the rain and the velocity of the rain relative to the car. So Ah, we can see that. Then the velocity of the rain relative to the car is equaling the velocity of the car to buy. To buy sign of theta S o the velocity of the rain relative to the car, 50 0.0 kilometers per hour, divided by sign of 60 degrees. This is equaling 57 points. 57.7 kilometers per hour. Therefore, the velocity of the rain with with respect to the cars 57.7 kilometers per hour, 60 degrees, uh, west of south. And then for part B, we could say that the velocity of the rain is equaling the velocity of the rain relative to the car Times Co sign of theta. This would be equaling 57.7 kilometers our times co sign of 60 degrees. And so the velocity of the rain is equaling 28 0.9 kilometers. For our this would be verdict vertically downwards. That is the end of the solution. Thank you for watching.