# Resultant Displacement - Vectors | Summary and Q&A

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August 16, 2022
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The Organic Chemistry Tutor
Resultant Displacement - Vectors

## TL;DR

Learn how to calculate the magnitude and direction of the resultant displacement using vector components and trigonometry.

## Key Insights

• π₯ Resultant displacement can be calculated by finding the magnitude and direction of the vector formed from the initial point to the final point of the motion.
• β The Pythagorean theorem is essential for calculating the magnitude of the resultant displacement, which is obtained by taking the square root of the sum of squared components.
• β£οΈ Breaking down vectors into x and y components allows for accurate calculations and the determination of the horizontal and vertical contributions to the resultant displacement.
• βΊοΈ The inverse tangent function is used to calculate the angle of the resultant displacement relative to the positive x-axis.
• π€± Different descriptions, such as north of east or south of west, can be used to specify the direction of the resultant displacement.
• β£οΈ Multiple vectors can be combined by adding their x and y components separately to obtain the overall resultant displacement.
• π The reference angle, found using inverse tangent, provides useful information for determining the direction of the resultant displacement.

## Transcript

in this video we're going to focus on solving problems that involve calculating someone's resultant displacement so let's work on this one karen walks 5 meters east and then 12 meters north so let's draw a picture so she travels 5 meters east and then 12 meters north what is the magnitude and direction of karen's resultant displacement to draw the ... Read More

### Q: How can we calculate the magnitude of the resultant displacement?

To calculate the magnitude, we use the Pythagorean theorem. The sum of the squared x and y components of the vectors involved gives us the magnitude of the resultant displacement, which can be found by taking the square root of this sum.

### Q: What is the significance of breaking vectors into x and y components?

Breaking vectors into x and y components allows us to accurately determine the resultant displacement. It helps us isolate the horizontal and vertical motion of the vectors and calculate their individual contributions to the final displacement.

### Q: How do we determine the direction of the resultant displacement?

The direction of the resultant displacement is determined by finding the angle between the resultant vector and the positive x-axis. This angle can be calculated using the inverse tangent function, also known as the arc tangent function.

### Q: What does it mean when the angle is measured as north of east or south of west?

When the angle is measured as north of east or south of west, it refers to the angle's orientation relative to the x-axis and y-axis. For example, north of east means the resultant displacement is above the positive x-axis and tilted towards the north in the counterclockwise direction.

## Summary & Key Takeaways

• The video explains how to calculate the magnitude and direction of resultant displacement using the Pythagorean theorem and trigonometric functions.

• Various examples are provided to demonstrate the calculation process for different scenarios involving multiple vectors.

• The video emphasizes the importance of breaking down vectors into their x and y components to accurately calculate the resultant displacement.

• The magnitude and direction of the resultant displacement are found using the square root of the sum of squared components and the inverse tangent function, respectively.