Sure, let's break down the problem step-by-step to calculate the total distance traveled and the displacement.
1. Analyze the Path:
- The boy goes 5 meters towards the east.
- Then, he moves 4 meters towards the north.
- Finally, he moves 2 meters towards the west.
2. Calculate the Net Movement in the East-West Direction:
- He initially moves 5 meters to the east and then 2 meters to the west.
- Net movement in the east-west direction = 5 meters east - 2 meters west = 3 meters east.
3. Determine Total Distance Traveled:
- Total distance is the sum of all individual distances traveled in each segment:
- Distance east: 5 meters
- Distance north: 4 meters
- Distance west: 2 meters
- Total distance = 5 meters + 4 meters + 2 meters = 11 meters.
4. Calculate Displacement:
- Displacement is the straight-line distance from the starting point to the final position.
- We have the net movement of 3 meters east and 4 meters north.
- To find the displacement, we use the Pythagorean theorem [tex]\( \text{Displacement} = \sqrt{(\text{net_east})^2 + (\text{north})^2} \)[/tex].
- Displacement = [tex]\( \sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \)[/tex] meters.
So, the total distance the boy traveled is 11 meters, and the displacement from the starting point is 5 meters.
