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Carnegie Mellon University

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Problem 52 Medium Difficulty

If raindrops are falling vertically at 7.50 $\mathrm{m} / \mathrm{s}$ , what angle from the vertical do they make for a person jogging at 2.25 $\mathrm{m} / \mathrm{s?}$

Answer

$\theta = 16.7 ^ { \circ }$

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Video Transcript

so we can create a small diagram. So is this. We have 33 vectors here. We have an angle here, theta and this vertically downwards is the velocity of Lorraine relative to the ground directly. Whores like sorry to the right, directly to the right or, in this case, to the Easter Easter positive X direction. Whatever you would like to call it, this would be the velocity of the person relative to the ground and then at an angle. Here we have the velocity of the rain relative to the person, and so we can say Fada would be equaling. Are 10 of the magnitude of the velocity of the person relative to the ground divided by the magnitude of the velocity of the rain relative to the ground. And we can say that then say that would be equal in our 10 of 2.25 meters per second. The velocity of the person relative to the ground, divided by the philosophy of Lorraine relative to the ground. 7.50 meters per second and this is equaling 16.7 degrees. So this would be the angle here of the rain relative to the person, 16.7 degrees. This would be our final answer. That is the end of the solution. Thank you for watching.

Carnegie Mellon University
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