a boy moves 3 metre towards east he then turns and moves 4 metre towards north calculate the distance travelled by the boy and displacement of the boy
Answers
Given :-
- A boy moves 3m towards East and then turns and moves 4m towards North.
Aim :-
- To calculate the distance travelled by the boy and the displacement of the boy.
Answer :-
What is Distance ?
- Distance is the initial path taken by the object to reach it's final position.
What is Displacement ?
Displacement is the shortest path between the initial and final position.
Distance and Displacement :
- Distance can be greater or equal to Displacement, It can never be less than Displacement itself.
- Distance can be either be positive or zero, while Displacement can be positive, negative or zero.
Solution :
(Refer to the image attached for the directions)
According to the question, the Boy travels East 3m, which means he travels right from the initial position. After reaching the point E, he turns 4m in the direction North which is the point N. The distance travelled is hence, 3m + 4m = 7m. The initial point is the point of intersection of NA and EW. This is the initial position. The path from initial position and point N, is the displacement. Notice that a triangle is formed where OB = Hypotenuse, OE = Base (assuming initial position to be 0) and EB = Height/Displacement.
By using the Pythagoras Theorem,
⇒ (OB)² = (OE)² + (EB)²
→ (OB)² = (4)² + (3)²
→ (OB)² = 16 + 9
→ (OB)² = 25
→ OB = √25m
Transposing the power,
→ OB = 5m
Therefore the Displacement is 5m and the Distance is 7m.
