Question

A person travels $100\text{km}$ in the North direction and then turns right and travels $100\text{km}$. The magnitude of displacement is

• A. $200\text{km}$
• B. $100\sqrt{2}\text{km}$
• C. $100\sqrt{3}\text{km}$
• D. None of these

Answer 1

The correct option is B $100\sqrt{2}\text{km}$


Assuming $O$ to be the initial position. Man travels $100\text{km}$ north (OA), turns right and travel $100\text{km}$ (AB)
$\therefore$ Displacement = OB (Line joining initial and final position)
By Pythagaros theorem,
Magnitude of displacement, $=\sqrt{(OA{)}^2+(AB{)}^2}$
$=\sqrt{{100}^2+{100}^2}=100\sqrt{2}\text{km}$