Nelson is walking towards his school. He first walks 3km in the east direction and then walks for 4km towards north. How much is Nelson’s displacement?
1) 7km in northeast direction
2) 1km in northeast direction
3) 5km in northeast direction
4) 5km in southeast direction
Answers
5 km in the northeast direction (option 3)
• Nelson first walks 3 km in the east direction and then walks 4 km toward the north.
• We need to find Nelson's displacement. As we know, displacement is defined as the shortest distance between the initial and the final position.
• In this case, let's take the starting point to be A, the point where Nelson stops after 3 km in the east direction to be B and the point where Nelson stops after 4 km walk in the north to be C.
• So, the displacement will be the distance AC.
Given,
AB = 3 km
BC = 4 km
To find,
AC =? (Displacement)
Solution,
Using Pythagoras theorem,
Hypotenuse² = Base² + height²
AC² = 3² + 4²
AC² = 9 + 16
AC² = 25
AC = 5 (The square root of 25 is 5)
• Nelson's direction after moving towards the east and then the north will be Northeast.
• Hence, 5 km in the northeast direction is the correct answer.