If you walk 3.0 km on a straight road and then find that you are 1.5 km east of your starting point and some unknown distance north of your starting point, in which of these directions did you walk?
To determine the direction you walked, we can use basic trigonometry. Since you walked 3.0 km on a straight road and ended up 1.5 km east of your starting point, you formed a right triangle with the hypotenuse being the distance you walked (3.0 km) and one leg being the distance you moved east (1.5 km).
To find the other leg of the right triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Therefore, we have:
(3.0 km)^2 = (1.5 km)^2 + (Unknown distance)^2
Simplifying the equation, we get:
9.0 km^2 = 2.25 km^2 + (Unknown distance)^2
Rearranging the equation, we have:
(Unknown distance)^2 = 9.0 km^2 - 2.25 km^2
(Unknown distance)^2 = 6.75 km^2
To solve for the unknown distance, we can take the square root of both sides:
Unknown distance = √(6.75 km^2)
Calculating the square root of 6.75 km^2, we find that the unknown distance is approximately 2.598 km.
Now that we know the unknown distance is approximately 2.598 km and the distance you moved east is 1.5 km, we can see that you moved farther north than east. Thus, you walked in a direction slightly north of east.
To determine the direction you walked, we can use the concept of displacement. Displacement is a vector quantity that represents the change in position from the initial point to the final point.
In this case, you walked 3.0 km on a straight road, which means the displacement is 3.0 km. Additionally, you ended up 1.5 km east of your starting point, which indicates a positive displacement in the east direction.
At this point, we can conclude that you walked in the east direction.