Question

A person travels 3 km in east direction, then he travels 4 km in South direction. what is the magnitude of displacement?
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Answer 1

As per the question , a person travels 3 km towards east then turns rightwards and travels 4 kilometre in the south direction.

To find:

Magnitude of displacement.

Concept:

Displacement is defined as the shortest length between the starting and stopping point. It is a vector having both magnitude and direction.

In this case , the displacement can be easily found out using Pythagoras theorem.

Calculation:

Magnitude of displacement be d :

$d = \sqrt{ {3}^{2} + {4}^{2} }$

$= > d = \sqrt{9 + 16}$

$= > d = \sqrt{25}$

$= > d = 5 \: km$

So displacement is 5 km.

Answer 2

Question -

A person travels 3 km in east direction, then he travels 4 km in South direction. what is the magnitude of displacement?

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Answer :-

We know that,

Displacement is the shortest length travelled between the initial point and the final point.

According to the given conditions, the displacement can be calculated using the Pythagoras Theorem.

$\displaystyle{\tt{d^2=3^2+4^2}}\\\\\displaystyle{\tt{\implies d^2=9+16}}\\\\\displaystyle{\tt{\implies d=\sqrt{25} }}\\\\\large\boxed{\displaystyle{\tt{\implies d=5\ km}}}$

∴ So, the magnitude of the displacement of the person is 5 km from his initial position.