A person travels 8 mi, due north, 3 mi, due west and 7 mi due south how far are they from were they started?
net displacement is 1 N and 3 W.
Use the Pythagorean Theorem (distance formula) to figure the diagonal distance (hypotenuse)
To find how far the person is from where they started, we can use the concept of vectors. We need to find the resultant displacement, which represents the straight-line distance from the starting point to the final position.
Let's break down the person's journey into three separate vectors: the northward displacement, the westward displacement, and the southward displacement.
The northward displacement is a vector of magnitude 8 miles in the positive y-direction (upward).
The westward displacement is a vector of magnitude 3 miles in the negative x-direction (leftward).
The southward displacement is a vector of magnitude 7 miles in the negative y-direction (downward).
To determine the net displacement, we can add these three vectors together. Considering the y-direction as positive and the x-direction as negative, the net displacement vector would be:
Net displacement = (0 miles, 8 miles + (-3 miles) + (-7 miles)) = (0 miles, -2 miles)
Here, the x-coordinate is 0 miles because there is no eastward or westward displacement.
Finally, to find the distance from the starting point, we take the magnitude of the net displacement vector:
Distance = sqrt((0 miles)^2 + (-2 miles)^2) = sqrt(0 + 4) = sqrt(4) = 2 miles
Therefore, the person is 2 miles away from where they started.