Question

A boy starts from his school and travels 3km east and then 4km towards north. find the displacement of the particle from initial to final position

Answer 1

the displacement of the particle from initial to final position = (square root of 3 + square root of 4 ) km
=5 km

Answer 2

The displacement of the boy from the initial to the final position is 5 km.

Given,

A boy starting from school travels:

3 km towards east,

then, 4 km towards the north.

To find,

Displacement from initial to the final position.

Solution,

It is given here that a boy who starts from his school travels:

towards east = 3 km, and then,

towards north = 4 km.

Refer figure.

Let S represents the school, and B be the final position of the boy. It can be observed that the boy will reach A after traveling 3 km towards east from his school at first, and then he travels 4 km towards north to reach B.

On joining S to B, we can see that, we get a right-triangle SAB, right-angled at A.

Now, the displacement will be SB, which can be determined by applying the Pythagoras theorem in ΔSAB.

Thus,

$SB^{2} =SA^{2} +AB^{2}$

Substituting the respective values, we get,

$SB^{2} =(3)^{2} +(4)^{2}$

$\implies SB^{2} =9+16=25$

$\implies SB =\sqrt{25}$

$\implies SB =5km.$

⇒ the displacement = 5 km.

Therefore, the displacement of the boy from the initial to the final position is 5 km.

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