Question

A cyclist follows the path from A to E as shown in the given diagram.


Calculate the distance and displacement with $1unit=2km$.

• A. $10\sqrt{2}\text{km}$ and $10\text{km}$
• B. $10\text{km}$ and $10\sqrt{2}\text{km}$
• C. $20\text{km}$ and $2\sqrt{10}\text{km}$
• D. $2\sqrt{10}\text{km}$ and $20\text{km}$

Answer 1

The correct option is C $20\text{km}$ and $2\sqrt{10}\text{km}$

To calculate the distance just add all the lengths of the line segments.
So, total distance is,
AB + BC + CD + DE = $8+4+6+2=20\text{km}$

To find the displacement, we use the Pythagoras theorem. The shortest path to reach E from A is a line joining A and E.

So, AE = $\sqrt{2^2+6^2}$ = $\sqrt{40}$ = 2$\sqrt{10}\text{km}$