Question

A person travels 3 km in east direction and then he travels 4 km in the south direction. What is the magnitude of displacement of the person? (1) 17 km (2) 13 km (3) 5 km (4) 0 km

Answer 1

$\sf \huge\underline {\green{ \underline{Answer :-}}}$

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.

$\bf \: {d}^{2} = {3}^{2} + {4}^{2}$

$\bf \implies \: {d}^{2} = 9 + 16$

$\bf \implies \: {d}^{2} = 25$

$\bf \implies \: d = \sqrt{25}$

$\bf \implies \: d = \sqrt{(5 \times 5)}$

$\bf \implies \:d = \sqrt{ {(5)}^{2} }$

$\: \: \: \: \: \boxed{\bf \implies \: d = 5 km}$

The displacement of the person is 5 km from his initial position.

Answer 2

As per question
Displacement will be the hypotenuse of right angle triangle formed,
Since Displacement is the shortest distance between final and initial position

Hence, Displacement = 5 km
Correct option is (3).