A person going for a walk follows the path shown in Figure...

Name: Problem 47, Chapter 3: Physics For Scientist and Engineers with Modern Physics
Uploaded: 2021-03-02T03:06:10-08:00
Duration: 1 min 42 s
Channel: Prashant Bana
Description: A person going for a walk follows the path shown in Figure P3.47. The total trip consists of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the starting point?

A person going for a walk follows the path shown in Figure P3.47. The total trip consists of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the starting point?

Key Concepts

Trigonometry

Trigonometry is crucial in vector analysis for relating angles to side lengths. It aids in determining the individual components of a vector based on its magnitude and direction, as well as in finding the angle of the resultant vector after combining multiple vectors.

Pythagorean Theorem

The Pythagorean theorem is used to calculate the resultant magnitude of a vector when its components are known. By treating the components as the legs of a right triangle, the theorem asserts that the square of the hypotenuse (the resultant displacement) is equal to the sum of the squares of the other two sides.

Displacement

Displacement is a vector quantity that represents the change in position of an object from its initial point to its final point. It accounts for both magnitude and direction, which differentiates it from distance, and it is independent of the path taken between these two points.

Vector Addition

Vector addition involves summing two or more vectors to determine a resultant vector. This process is essential in physics for combining multiple movements or forces by considering both their magnitudes and directions, often using graphical methods like the head-to-tail approach or analytical methods by summing individual components.

Components of a Vector

Breaking a vector into its perpendicular components, typically along the horizontal and vertical axes, simplifies the process of vector addition and analysis. This decomposition allows for separate computation of the effects in each direction and is foundational when applying trigonometric functions to solve for magnitudes and angles.

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