Answered: A ship sailing in the Gulf Stream is…

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 ship sailing in the Gulf Stream is heading 25.0∘ west of north at a speed of 4.00 m/s relative to the water. Its velocity relative to the Earth is 4.80 m/s at an angle 5.00∘ west of north.

A) What is the magnitude of the velocity of the Gulf Stream in meters per second? (The velocity obtained is typical for the Gulf Stream a few hundred kilometers off the east coast of the United States.)

B) What is the angle of the velocity of the Gulf Stream in degrees north of east?

Expert Solution

Step 1

To calculate the magnitude and direction of the velocity of the Stream.

Given:
Magnitude of velocity of the ship with respect to the water: $v_{S W} = 4.00 m/s$
Angle made by the velocity $v_{S W}$ : $θ_{S W} = 25.0 °$ west of north
Magnitude of velocity of the ship with respect to the Earth: $v_{S E} = 4.80 m/s$
Angle made by the velocity $v_{S E}$ : $θ_{S E} = 5.00 °$ west of north

To calculate:
A) Magnitude of the velocity of the Stream with respect to the Earth: $v_{W E}$
B) Angle of the velocity $θ_{W E}$ north of east.

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