In going from one city to another, a car travels 75 km north, 60 km north-west and 20 km east

step 1 In this question we learn about some basic concept of the vectors. The question is in going from

In going from one city to another, a car travels 75 km...

In going from one city to another, a car travels $75 \mathrm{~km}$ north, $60 \mathrm{~km}$ north-west and $20 \mathrm{~km}$ east. The magnitude of displacement between the two cities is (take $1 \sqrt{2}=0.7)$ (A) $170 \mathrm{~km}$ (B) $137 \mathrm{~km}$ (C) $119 \mathrm{~km}$ (D) $140 \mathrm{~km}$

In going from one city to another, a car travels $75 \mathrm{~km}$ north, $60 \mathrm{~km}$ north-west and $20 \mathrm{~km}$ east. The magnitude of displacement between the two cities is (take $1 \sqrt{2}=0.7)$
(A) $170 \mathrm{~km}$
(B) $137 \mathrm{~km}$
(C) $119 \mathrm{~km}$
(D) $140 \mathrm{~km}$

Key Concepts

Pythagorean Theorem

The Pythagorean theorem is used to determine the magnitude of the resultant displacement once the individual x and y components have been summed. It calculates the total displacement as the square root of the sum of the squares of its components.

Coordinate System

A coordinate system is used to describe the directions involved in a displacement problem. By assigning directions such as north, east, and others as axes, each displacement is represented by its x (horizontal) and y (vertical) components to facilitate their addition.

Decomposition into Components

Decomposition into components involves breaking down vectors into perpendicular parts, typically along the x (east-west) and y (north-south) axes. Directions that are not aligned with the primary axes, like northwest, need to be resolved into these components using trigonometric relationships.

Displacement

Displacement is a vector quantity that refers to the change in position of an object. It is not the total distance traveled, but rather the straight-line distance from the starting point to the end point, including the direction of movement.

Vector Addition

Vector addition is the process of combining two or more vectors to produce a resultant vector. In problems involving multiple segments of a journey, individual displacements are added component-wise to determine the overall displacement.

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