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Q14.

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Physics Principles with Applications
Found in: Page 69
Physics Principles with Applications

Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922

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Short Answer

Suppose a vector V→ makes an angle ϕ with respect to the y-axis. What could be the x and y components of vector V→?

The x and y components of vector V→ are Vsinϕ and Vcosϕ, respectively.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1. Significance of the vector components

A vector can be divided into two or three components depending upon the coordinate axes. The vector can be split into two or three scalar forms of quantities.

The components of the vector can be generally obtained when the vector is inclined at some angle with any of the coordinate’s axes.

The resultant of two or more vectors can be calculated with the help of the addition or the subtraction of the horizontal and vertical components of the individual vectors.

Step 2. Procedure for the determination of the components of vector V→

Consider that the Cartesian coordinates system consists of x and y-axes. Vector V→ is making an angle of ϕ with the y-axis. Then, vector V→ is broken into two components along the x and y-axes.

While resolving any of the vectors, it can be noted that the axis with which the vector is inclined is considered the (cosine) component of the same vector. The other axis could be considered the (sine) component of the same vector.

It is given that vector V→ is inclined with the y-axis. So, the y-axis consists of the (cosine) component, and therefore, the other axis, that is, the x-axis, can be taken as the (sine) component of V→ vector.

Step 3. The determination of the components of vector V→

The x-component of vector V→ can be expressed as

Vx=Vsinϕ.

Here, Vx is the x-component of the V→, ϕ is the angle of inclination of the vector with the y-axis, and V is the magnitude of the vector.

The y-component of vector V→ can be expressed as

Vy=Vcosϕ.

Here, Vy is the y-component of the vector V→, and ϕ is the angle of inclination of the vector with the y-axis.

Thus, the x and y components of vector V→ are Vsinϕ and Vcosϕ, respectively.

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