Physics :adaobi walked 2km due west and then 2km due south. Calculate the displacement of the girl.
on an x y coordinate system
x = -2
y = -2
the magnitude is sqrt (4+4) = 2 sqrt(2)
the direction is 45 degrees below -x axis
= 180 + 45
= 225 degrees counterclockwise from +x axis
To calculate the displacement of the girl, we can use the Pythagorean theorem.
First, let's draw a diagram to visualize the situation. We start with the point of origin (O), where Adaobi starts walking, and then plot her movements.
Step 1: Adaobi walks 2 km due west. We can represent this as a horizontal line going to the left, with a length of 2 km. Let's call this point A.
Step 2: Adaobi walks 2 km due south. We can represent this as a vertical line going downwards, with a length of 2 km. Let's call this point B.
Now, we can draw a right triangle with O as the right angle. The horizontal line (OA) represents the displacement due west, and the vertical line (OB) represents the displacement due south.
We can calculate the displacement (OC) using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Applying the theorem, we have:
OC^2 = OA^2 + OB^2
Substituting the values, we get:
OC^2 = (2 km)^2 + (2 km)^2
OC^2 = 4 km^2 + 4 km^2
OC^2 = 8 km^2
To find OC, we take the square root of both sides:
OC = √(8 km^2)
OC ≈ 2.83 km
Therefore, the displacement of Adaobi is approximately 2.83 km in a direction that is a combination of west and south.