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

step 1 We will learn about some basic concept of the vectors. The question is in going from one city to

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 magni- tude 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 magni- tude 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. $140 \mathrm{~km}$

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Key Concepts

Trigonometric Approximations

Trigonometric approximations simplify calculations when working with angles that yield irrational numbers. For example, approximating values like 1/?2 as 0.7 can help estimate the components of vectors oriented at angles such as 45°.

Pythagorean Theorem

The Pythagorean theorem is used to calculate the magnitude of a resultant vector when its perpendicular components are known. By squaring and summing the components and taking the square root of the result, the overall magnitude of displacement can be determined.

Displacement

Displacement represents the shortest distance from the starting point to the ending point of an object's motion, taking into account both magnitude and direction. It is a vector quantity that differs from distance, which is the total path length traveled.

Vector Addition

Vector addition is the process of combining two or more vectors to determine a resultant vector. This is done by summing the individual vectors' components, which allows calculation of a net effect when different movements or forces are applied.

Component Decomposition

Component decomposition involves breaking a vector into its perpendicular components, typically along horizontal and vertical directions. This makes it easier to add vectors together, especially when they are not aligned with the coordinate axes.

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