Question

A boy travels 3km north and then 4km east. what will be:
a) the distance traveled by him?
b) the minimum distance he needs to go to get back to where he started?
c) the direction of his displacement ?

Answer 1

1: 7km

2: 7km

3: north east

but not sure

Answer 2

Answer :-

♦ Before solving we must know :-

• What is distance ?

>> The length of path covered is called distance

• What is displacement ?

>> The shortest distance between two points

• What is the angle between two consecutive cardinal directions ?

>> The angle is 90°

♦ Solution :-

♦ Given that

• Distance traveled :- 4 km East , 3 km North

♦ So distance traveled

= 4 + 3

= 7 km

♦ Minimum Distance traveled (consider attached)

• As The cardinal direction makes 90°

• Then displacement = Distance between end points or hypotenuse of the ∆

• Then by using Pythagorean Theorem

Hypotenuse = $\sqrt{ (Perpendicular)^2 + (Base )^2 }$

>> Perpendicular = 4 km

>> Base = 3 km

• By substituting the values

Hypotenuse = $\sqrt{ (4)^2 + (3)^2 }$

$\implies$ Hypotenuse = $\sqrt{ 16 + 8}$

$\implies$ Hypotenuse = $\sqrt{ 25}$

$\implies$ Hypotenuse = 5 km

Or minimum distance = 5 km

♦ Direction of Displacement

= North - East ( From the diagram)