from point A, a boy walks 4 m to the east,2 m to the sout, 4 m to the west , and finally, 2 m to the north , find the distance he travelled and his displacement
distance = 4 + 2 + 4 + 2 = 12 m.
Displacement = Df-Do = 0-0 = 0.
Df = Final distance.
Do = Starting point.
To find the distance traveled, we need to add up the lengths of all the paths taken by the boy.
Step 1: The boy walks 4 m to the east.
Step 2: The boy walks 2 m to the south.
Step 3: The boy walks 4 m to the west.
Step 4: The boy walks 2 m to the north.
Distance traveled = 4 m + 2 m + 4 m + 2 m
Distance traveled = 12 meters
To find the displacement, we need to calculate the straight-line distance and direction from the starting point to the final point.
Step 1: The boy walks 4 m to the east (moves to point B).
Step 2: The boy walks 2 m to the south (moves to point C).
Step 3: The boy walks 4 m to the west (moves back to point D).
Step 4: The boy walks 2 m to the north (moves back to the starting point A).
Displacement is the straight-line distance between the starting point (A) and the final point (A). Since the boy ends up at the starting point, the displacement is zero.
Displacement = 0 meters
To find the distance traveled by the boy, we need to calculate the sum of the distances covered in each direction.
From Point A, the boy walks:
- 4 m to the east
- 2 m to the south
- 4 m to the west
- 2 m to the north
Now, let's calculate the distance traveled:
Distance traveled = Distance covered in the east direction + Distance covered in the west direction + Distance covered in the south direction + Distance covered in the north direction
Distance traveled = 4 m + 4 m + 2 m + 2 m
Distance traveled = 12 meters.
So, the boy traveled a total distance of 12 meters.
Now, let's calculate the displacement, which is the straight-line distance from the starting point to the final point.
To calculate displacement, we need to find the vector sum of the individual displacements in both the x and y directions.
From Point A, the boy walks:
- 4 m to the east
- 2 m to the south
- 4 m to the west
- 2 m to the north
To calculate the displacement in the x-direction, we subtract the distance traveled west from the distance traveled east:
Displacement in the x-direction = Distance traveled east - Distance traveled west
Displacement in the x-direction = 4 m - 4 m
Displacement in the x-direction = 0 meters
To calculate the displacement in the y-direction, we subtract the distance traveled south from the distance traveled north:
Displacement in the y-direction = Distance traveled north - Distance traveled south
Displacement in the y-direction = 2 m - 2 m
Displacement in the y-direction = 0 meters
Finally, we can calculate the displacement using the Pythagorean theorem:
Displacement = sqrt((Displacement in the x-direction)^2 + (Displacement in the y-direction)^2)
Displacement = sqrt((0)^2 + (0)^2)
Displacement = 0 meters
Therefore, the boy's displacement is zero meters, meaning he ended up back at Point A.