Answered: What are the trig equations we use to…

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 47P: For vectors and , calculate (a) and its magnitude and direction angle, and (b) and its magnitude and...

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Question

What are the trig equations we use to find a vector's x and y components, and it's directional angle?

Expert Solution

Step 1

Any vector directed in two dimensions can be thought of having an influence in two different directions, i.e., it can be thought of having two parts, each part of a 2-dimensional vector is known as a component.

For example, in the vector $5 \hat{i} + 2 \hat{j}$ , the x-axis (horizontal) component is 5 and y-axis (vertical) component is 2.

Step 2

Consider a vector $\vec{F}$ as shown below,

Draw a perpendicular from tip of vector $\vec{F}$ on x-axis, then $\vec{F_{x}}$ is the projection of $\vec{F}$ on x-axis. Similarly, $\vec{F_{y}}$ is the projection of $\vec{F}$ on y-axis.

Magnitude of $\vec{F_{x}}$ tells how much of much $\vec{F}$ exists in x-direction and magnitude of $\vec{F_{y}}$ tells how much of $\vec{F}$ exists in y-direction.

Also, graphically we have $\vec{F}$ = $\vec{F_{x}}$ + $\vec{F_{y}}$ and these three vectors form a right angle triangle.

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