Question

A vector has components $A_{x}=54 \mathrm{m}$ and $A_{y}=23 \mathrm{m}$. Find the length of the vector $\vec{A}$ and the angle it makes with the $x$ axis.

Name: Problem 47, Chapter 1: College Physics: Reasoning and Relationships
Uploaded: 2022-02-15T04:30:19-08:00
Duration: 1 min
Channel: Raj Bala
Description: A vector has components Ax=54 m and Ay=23 m. Find the length of the vector A⃗ and the angle it makes with the x axis.

   A vector has components $A_{x}=54 \mathrm{m}$ and $A_{y}=23 \mathrm{m}$. Find the length of the vector $\vec{A}$ and the angle it makes with the $x$ axis.

College Physics: Reasoning and Relationships

Nicholas J.… 2nd Edition

Chapter 1, Problem 47

Instant Answer

Solved by Expert Raj Bala

02/15/2022

Step 1

Here, $A_{x}$ and $A_{y}$ are the components of the vector along the x and y axes respectively. Show more…

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A vector has components $A_{x}=54 \mathrm{m}$ and $A_{y}=23 \mathrm{m}$. Find the length of the vector $\vec{A}$ and the angle it makes with the $x$ axis.

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Key Concepts

Vector Components

Vector components refer to the representation of a vector in terms of its individual parts along defined axes, such as the x-axis and y-axis. This breakdown allows for easier computation of the vector's properties, such as its magnitude and direction.

Vector Magnitude

The magnitude of a vector is determined by using the Pythagorean theorem, which calculates the length of the vector as the square root of the sum of the squares of its components. This concept is crucial for understanding the overall size or strength of the vector irrespective of its direction.

Angle Calculation

Determining the angle of a vector typically involves using trigonometric functions, in particular the inverse tangent (arctan), which relates the ratio of the vector's y-component to its x-component to the angle it makes with the x-axis. This helps in analyzing the directional properties of the vector in a coordinate system.

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