you first walk 8.0km north from home then walk east until your displacement from home is 10.0 km. How far east did you walk?
To find out how far east you walked, we can break down your displacement into its north and east components.
First, let's consider the northward movement. You walked 8.0 km north, so your displacement in the north direction is 8.0 km.
Next, let's determine the remaining eastward displacement. Overall, your displacement from home is 10.0 km. Since you walked 8.0 km north already, the remaining displacement in the east direction is the difference between the total displacement and the northward displacement.
Remaining displacement in the east direction = Total displacement - Northward displacement
Remaining displacement in the east direction = 10.0 km - 8.0 km
Remaining displacement in the east direction = 2.0 km
Therefore, you walked 2.0 km east.
Assuming you are not near the poles, you can calculate the distances by the Pythagoras theorem.
North and east are perpendicular to each other, and the hypothenuse sought is 10 km, with one leg being 8 km. What is the length of the other leg, x, if according to Pythagoras,
10^sup2; = 8² + x²