a child walks 5m south then 12m east He again walks 5m north what is his displacement
5mS and 5m N cancel each other.
So, all that's left is the distance east.
Plot the route on some graph paper to see this.
D = -5i+12+5i = 12+0 = 12 m.
To find the displacement of the child, we need to determine the net distance and direction from the starting point to the ending point.
First, let's represent the child's movements on a coordinate plane.
Starting from the origin (0,0), the child walks 5m south, which means the child's position will be at (0,-5).
Next, the child walks 12m east, so the new position will be (12,-5).
Finally, the child walks 5m north, which brings the final position to (12,0).
To calculate the displacement, we need to find the straight-line distance from the starting point to the ending point.
Using the Pythagorean theorem, we can calculate the displacement:
Displacement = √(change in x)^2 + (change in y)^2
change in x = 12 - 0 = 12
change in y = 0 - (-5) = 5
Displacement = √(12^2 + 5^2)
= √(144 + 25)
= √169
= 13
Therefore, the child's displacement is 13 meters.
To find the displacement of the child, we need to find the net distance and direction from the starting point to the ending point.
Let's break down the child's movements step by step:
1. The child walks 5m south.
- This means the child moves 5 meters in the opposite direction of the north.
- So, the child is at -5m in the vertical direction (south).
2. Then, the child walks 12m east.
- This means the child moves 12 meters in the right direction (east).
- So, the child is at +12m in the horizontal direction (east).
3. Lastly, the child walks 5m north.
- This means the child moves 5 meters in the opposite direction of the south.
- As the child was already at -5m in the vertical direction, walking 5m north cancels out the initial displacement.
- So, the child ends up at 0m in the vertical direction.
Since the child ends up at 0m vertically and 12m horizontally, the final displacement can be calculated using the Pythagorean theorem:
Displacement = √(vertical displacement² + horizontal displacement²)
Displacement = √(0² + 12²)
Displacement = √(0 + 144)
Displacement = √144
Displacement = 12m
Therefore, the child's displacement is 12 meters to the east.