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

Key Concepts

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.

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.

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.

Transcript

00:01 Hello strains in this problem we have given a person going for a walk follows the path.

00:07 So first we will draw the diagram.

00:10 Suppose this is the initial point.

00:12 A starting point.

00:14 It goes this is ah, ex accessible is and this is why access in horse the positive extraction 100 m and then it goes 300 m in the negative y direction.

00:37 This is three and millimeters and then it goes 1 50 m below the negative x axis 1 50 m.

01:03 This angle is 30 degrees and then it goes 200 m.

01:17 60 degree of of the whole region.

01:20 This is the yeah, supposed to 100 m.

01:28 We have to find the displacement within 10 displacement missile from the starting point.

01:40 Right? so how we'll solve this? first of all, the will draw the confident, this confident and this confident.

01:55 Suppose this is why and this is x so x will be equal toe 1 50 cost 30 and why will be equal toe or 1 50 scientific? so this will be equal to 75 this will be equal to and we saw this.

02:17 We get the value off 1 50 cost 30 this will be called to 1 29.9.

02:28 Meet that now again, we will this distance a bles y prime and distances explain.

02:40 So this angle is given 60 degree, so the explain will be equal toe 200 core 60.

02:51 This will be equal to 100 m.

02:59 And why brian will be called 202.

03:01 Science 60.

03:04 Sorry.

03:04 202,016.

03:07 So this will be equal toe.

03:10 Hi.

03:12 This will be equal to 1 73.2 m.

03:16 Now we know that the result and displacement will be this.

03:29 Okay, we have to find this distance and this distance this total distance is equal to from suppose this is a negative x axis the total distance from this point.

03:56 From this point to this point, this total distance will be equal.

03:59 Toe 300.

04:01 Let's lie.

04:03 And this distance, i suppose this is e...

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