(1)A girl walks 10m due west and 15m due south. What is her displacement? (2)A boy walked a distance of 18m northwards, 7m eastward and 9m southward. what is her total displacement?
1. displacement=10W+15S
2. add them. But how did the boy turn into a girl? Is he a sissy?
To find the displacement of the girl in the first scenario, we can use the Pythagorean theorem. Displacement is the straight-line distance from the starting point to the ending point, regardless of the path taken.
Given that the girl walks 10m due west and 15m due south, we can create a right-angled triangle with the west distance as the base and the south distance as the height. This triangle represents the displacement.
Using the Pythagorean theorem, we can calculate the hypotenuse of the triangle (the displacement) as follows:
Displacement = √(base² + height²)
Displacement = √(10² + 15²)
Displacement = √(100 + 225)
Displacement = √(325)
Displacement ≈ 18.03m
Therefore, the girl's displacement is approximately 18.03m.
Now, let's move on to the second scenario.
To find the total displacement of the boy in the second scenario, we need to consider the distances traveled in different directions. For simplicity, we can represent north as positive, east as positive, and south as negative.
The boy walked a distance of 18m northwards (+18m), 7m eastwards (+7m), and 9m southwards (-9m). To find the total displacement, we need to calculate the net distance in both the north-south and east-west directions.
In the north-south direction:
Net distance = total distance north - total distance south
Net distance = 18 - 9
Net distance = 9m northwards
In the east-west direction:
Net distance = total distance east - total distance west
Net distance = 7 - 0 (no westward distance mentioned)
Net distance = 7m eastwards
Therefore, the boy's total displacement is 9m northwards and 7m eastwards.
Note: Displacement is different from distance traveled. Displacement considers the straight-line distance between the starting and ending points, while distance traveled is the total distance covered without considering direction.