Question

A boy travels 5 km to the south and turns west to travel 13 km. Finally, he travels on the same path, 9 km due east and stops. What is his displacement from the initial point?

• A. $\sqrt{41}$ km South-east
• B. $\sqrt{41}$ km North-west
• C. $\sqrt{41}$ km South-west
• D. $\sqrt{41}$ km North-east

Answer 1

The correct option is C

$\sqrt{41}$ km South-west

DA denotes the 5 km that the boy travelled south. Then he turned to the west and travels 13 km which is denoted by AB.

He returns on the same path while travelling 9 km east which is his destination.

Effectively, he travelled 4 km west which is shown using AC.

Displacement is DC

Displacement DC=$\sqrt{D{A}^2+A{C}^2}$

= $\sqrt{5^2+4^2}$

= $\sqrt{41}$ km South-west