John walks 5m south and 5m west. Calculate john's distance and displacement from the starting point.
distance is just 5+8
Use the distance formula (Pythagorean Theorem) to figure the displacement.
To calculate John's distance from the starting point, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, John walks 5 meters south and 5 meters west. We can visualize this as a right-angled triangle, where the south direction is represented by the vertical side, and the west direction is represented by the horizontal side. The distance John travels is the length of the hypotenuse.
Using the Pythagorean theorem, we can calculate the distance John traveled as follows:
Distance = √(5^2 + 5^2)
= √(25 + 25)
= √50
≈ 7.07 meters
So, John's distance from the starting point is approximately 7.07 meters.
Now let's calculate John's displacement. Displacement is a vector quantity that represents the straight-line distance and direction from the starting point to the ending point. It can be calculated by finding the straight-line distance between the starting and ending points using the Pythagorean theorem, as we did above, and then considering the direction.
Since John walks 5 meters south and 5 meters west, the displacement can be calculated as follows:
Displacement = √((0 - (-5))^2 + (0 - (-5))^2)
= √(5^2 + 5^2)
= √(25 + 25)
= √50
≈ 7.07 meters
The direction of the displacement can be determined from the angle of the line connecting the starting and ending point with respect to a reference direction (e.g., north). In this case, John's displacement is 45 degrees southwest from the starting point.
So, John's displacement from the starting point is approximately 7.07 meters in the southwest direction.