Problem 2A river that is 500 meters wide flows due west at 8 m/s. A boat leaves the southern bank of theriver. The velocity vector of the boat with respect to the ground points 60 degrees north of west.The constant speed of the boat relative to the ground is 0.642 m/s. What is the velocity vector ofthe boat relative to the river? Choose east to point in the positive x direction and north to pointalong the positive y-axis. Give your answer in units of m/s, Cartesian coordinates (in terms of i andj) and to 2 significant figures.MacBook Airesc吕0000000888DIIDDF1F2F3F4F5F6F7F8F9F10F112324&08.QEY.AGJK+ I/F.7.

Given: width of the river = 500 m Speed of river, vr→=8 m/s due west =-8i^ vbg→ speed of boat…

Answered: Problem 2 A river that is 500 meters…

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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Problem 2
A river that is 500 meters wide flows due west at 8 m/s. A boat leaves the southern bank of the
river. The velocity vector of the boat with respect to the ground points 60 degrees north of west.
The constant speed of the boat relative to the ground is 0.642 m/s. What is the velocity vector of
the boat relative to the river? Choose east to point in the positive x direction and north to point
along the positive y-axis. Give your answer in units of m/s, Cartesian coordinates (in terms of i and
j) and to 2 significant figures.
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Expert Solution

Step 1

Given:

width of the river = 500 m
Speed of river, $\vec{v_{r}} = 8 m / s due west = - 8 \hat{i}$
$\vec{v_{bg}}$ speed of boat relative to ground $= 0.642 m / s$

So, the velocity of boat relative to ground in vector form will be given as:

$\begin{array}{rcl} \vec{v_{bg}} & = & 0.642 \times (\cos 60 °) \times (- \hat{i}) + 0.642 \times (\sin 60 °) \times (\hat{j}) \\ = & - 0.321 \hat{i} + 0.556 \hat{j} \end{array}$

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