Explanation Given: A local coordinate system at latitude L on the earth’s surface with east, north, and up as the x , y , and z directions respectively. The earth’s angular velocity vector is given by Ω = 〈 0 , ω cos L , ω sin L 〉 The wind vector is given by w = 〈 w 1 , w 2 , 0 〉 and Coriolis force vector is given by F c = − 2 m Ω × w Formula used: If two vectors a and b are given by a = 〈 a 1 , a 2 , a 3 〉 and b = 〈 b 1 , b 2 , b 3 〉 Then the cross product a × b is given by a × b = | i j k a 1 a 2 a 3 b 1 b 2 b 3 | = ( a 2 b 3 − a 3 b 2 ) i − ( a 1 b 3 − a 3 b 1 ) j + ( a 1 b 2 − a 2 b 1 ) k Calculation: Consider the angular velocity vector To determine (b) To show: The x and y components of the equation − V ∇ p + F c = 0 are V p x = 2 m ω ( sin L ) w 2 and V p y = − 2 m ω ( sin L ) w 1 respectively.

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ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 14.5, Problem 44E

To determine

(a)

To find:

The components of the Coriolis force vector.

To determine

(b)

To show:

The x and y components of the equation −V∇p+Fc=0 are Vpx=2mω(sinL)w2 and Vpy=−2mω(sinL)w1 respectively.

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Chapter 14.5, Problem 43E

Chapter 14.5, Problem 45E

Chapter 14 Solutions

Calculus: Early Transcendentals

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

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(a) To find: The components of the Coriolis force vector .

Solution Summary: The author explains how to find the components of the Coriolis force vector based on a local coordinate system at latitude L on the earth's surface.

Videos

(a)

To find:

The components of the Coriolis force vector.

(b)

To show:

The x and y components of the equation −V∇p+Fc=0 are Vpx=2mω(sinL)w2 and Vpy=−2mω(sinL)w1 respectively.

Want to see the full answer?

Chapter 14 Solutions

(a) To find: The components of the Coriolis force vector .

Solution Summary: The author explains how to find the components of the Coriolis force vector based on a local coordinate system at latitude L on the earth's surface.

Videos

(a) To find: The components of the Coriolis force vector.

(b) To show: The x and y components of the equation −V∇p+Fc=0 are Vpx=2mω(sinL)w2 and Vpy=−2mω(sinL)w1 respectively.

Want to see the full answer?

Chapter 14 Solutions

(a)

To find:

The components of the Coriolis force vector.

(b)

To show:

The x and y components of the equation −V∇p+Fc=0 are Vpx=2mω(sinL)w2 and Vpy=−2mω(sinL)w1 respectively.