An object is moving at 18 m / s at 220^∘ counterclockwise from the x -axis. Find the x - and y -

Name: Problem 21, Chapter 3: Essential University Physics
Uploaded: 2020-05-18T21:01:31-08:00
Duration: 2 min 28 s
Channel: Whitney Massock
Description: An object is moving at 18 m / s at 220^∘ counterclockwise from the x -axis. Find the x - and y -components of its velocity.

step 1 So we have an object that's moving at 18 meters per second at 220 degrees counterclockwise of ou

Question

An object is moving at $18 \mathrm{m} / \mathrm{s}$ at $220^{\circ}$ counterclockwise from the $x$ -axis. Find the $x$ - and $y$ -components of its velocity.

   An object is moving at $18 \mathrm{m} / \mathrm{s}$ at $220^{\circ}$ counterclockwise from the $x$ -axis. Find the $x$ - and $y$ -components of its velocity.

Essential University Physics

Richard Wolfson 3rd Edition

Chapter 3, Problem 21

Instant Answer

Solved by Expert Whitney Massock

05/18/2020

Step 1

The object is moving at $220^{\circ}$ counterclockwise from the x-axis. However, in trigonometry, it's often easier to work with angles that are less than $90^{\circ}$. We can find such an angle by subtracting $220^{\circ}$ from $270^{\circ}$ (the angle that would Show more…

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An object is moving at $18 \mathrm{m} / \mathrm{s}$ at $220^{\circ}$ counterclockwise from the $x$ -axis. Find the $x$ - and $y$ -components of its velocity.

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Key Concepts

Trigonometric Functions in Vector Analysis

Trigonometric functions such as cosine and sine are essential in vector decomposition, as they relate the angle and magnitude of a vector to its horizontal and vertical components. Cosine gives the proportion of the magnitude along the x-axis, while sine gives the proportion along the y-axis.

Coordinate System and Angle Measurement

Understanding the standard Cartesian coordinate system and how angles are measured counterclockwise from the x-axis is crucial. This knowledge ensures that the signs and directions of the calculated components correctly represent the vector's orientation in the plane.

Vector Decomposition

This is the process of breaking a vector into its constituent parts along mutually perpendicular axes (usually x and y). It allows complex motion or force directions to be analyzed in terms of simpler, one-dimensional effects.

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