A person travels 4 meters North 6 meters West and 4 meters South. what is the total displacement?
4 north cancels 4 south
so total is 6 west
To find the total displacement, we need to calculate the net distance and direction from the starting point to the ending point.
First, let's assign positive (+) values for north and east directions and negative (-) values for south and west directions.
The person travels 4 meters North, which can be represented as +4 in the vertical (North-South) direction.
Then, they travel 6 meters West, which can be represented as -6 in the horizontal (East-West) direction.
Finally, they travel 4 meters South, which can be represented as -4 in the vertical direction.
Now, to calculate the total displacement, we need to add the north-south and east-west components together.
In the vertical direction, +4 meters North and -4 meters South cancel each other out, resulting in 0 displacement.
In the horizontal direction, we have -6 meters West.
Therefore, the total displacement is -6 meters West. It means the person ends up 6 meters to the west of their starting point.
To find the total displacement, we need to calculate the net distance and direction traveled.
Step 1: Determine the horizontal displacement:
The person travels 6 meters to the west. Since west is opposite to the positive x-axis, the displacement in the x-direction is -6 meters.
Step 2: Determine the vertical displacement:
The person travels 4 meters to the north and then 4 meters to the south. Thus, the vertical displacement is 4 - 4 = 0 meters.
Step 3: Calculate the total displacement:
Using the Pythagorean theorem, we can calculate the magnitude of the displacement as the square root of the sum of the squares of the horizontal and vertical displacements:
Displacement = sqrt((-6)^2 + 0^2)
Displacement = sqrt(36 + 0)
Displacement = sqrt(36)
Displacement = 6 meters
So the total displacement is 6 meters.