Answered: A river 279 m wide flows at a uniform…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A river 279 m wide flows at a uniform 2.8 m/s east. Mary can row her boat at a constant speed of 3.5 m/s relative to the moving water. She wants to row her boat due north directly across the river. A. Calculate the direction that Amy should head the boat. Express the result using points of the compass and an angle.

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Step 1

Given

The width of the river is $d = 279 (m)$

the velocity of the river in the east direction is $v_{r} = 2.8 (m / s)$

the velocity of the boat relative to the river is $v_{b r} = 3.5 (m / s)$

She wants to travel in the north direction. So she has to row her boat upstream.

So the component of the velocity of the boat relative to the river in the north direction is $v_{b r, y} = 3.5 (m / s) \cos θ$

So the component of the velocity of the boat relative to the river in the east direction is $v_{b r, x} = - 3.5 (m / s) \sin θ$

and the component of the velocity of the river in the east direction is $v_{r, x} = 2.8 (m / s)$

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