Question

a person Travels 4 km towards east and then 3 km towards north what is the distance travelled and displacement of the person​

Answer 1

Answer:

Explanation:

Distance covered is 4+3 = 7km.

Displacement can be calculate by imagining the person's path as a triangle, with sides 4, 3, and x where,

4 = base of triangle= A

3 = height of triangle= B

x = hypotenuse  (we know it is a right angle triangle since east and north           directions are at 90° with each other.)

Here, x is the displacement since it is the shortest path from A to B.

Using pythagoras theorem,

$A^{2} + B^{2} = x^{2}$

$4 ^{2} + 3^{2}$ = 16 + 9 = 25 = $x^{2}$

Therefore, x= 5.

You can also do this with vectors,

x =$\sqrt{(3)^{2}j +4^{2}i }$ = 5.

Answer 2

[Refer to the attachment for diagram]

AnswEr :

Given that a person travels 4 km towards East & then 3 km towards North.

We have to find total distance covered and displacement of person.

From the data we can easily say that :

As the person travels 4 km towards East and then 3 km towards North, so total distance will be equal to (AB + BC)

→ Total distance = AB + BC

→ Total distance = 4 + 3

→ Total distance = 7 km

∴ Total distance covered = 7 km (Ans : 1)

Now refer to the attachment, according to question we can say that displacement will be equal to AC.

Now according to Pythagoras theorem i.e. Hypotenuse² = Base² + Altitude²

According to question :

→ AC² = AB² + BC²

→ AC² = 4² + 3²

→ AC² = 16 + 9

→ AC² = 25

→ AC = √25

→ AC = 5 km

∴ Total displacement of person = 5 km (Ans : 2)