Benjamina started her walk from the front door of her ground floor apartment. She walked 6 meters to the corner of the building and then turned the corner and walked 10 meters to her friend’s apartment. Identify the difference between the distance she walked and her displacement.
The difference between the distance she walked and her displacement is that the distance she walked is 16 meters, while her displacement is only 10 meters. Displacement is the total distance moved from the starting point, regardless of the direction taken.
To find the difference between the distance Benjamina walked and her displacement, we need to understand the concepts of distance and displacement.
Distance is the actual path or length traveled by an object. It is always a positive value and does not consider the direction of motion. In this case, we can calculate the distance by adding the distances she walked in each step:
Distance = 6 meters + 10 meters = 16 meters.
Displacement, on the other hand, is the shortest distance between the initial and final positions, along with the direction of motion. It can be positive, negative, or zero, depending on the direction of travel. Displacement can be calculated using vector addition or the Pythagorean theorem.
In this scenario, Benjamina started at her front door and ended at her friend's apartment. Let's assume that the front door is the origin (0,0) on a coordinate system.
She walked 6 meters to the corner of the building, which we can represent as a vector [(6, 0)].
Then, she turned the corner and walked 10 meters to her friend's apartment, represented as another vector [(0, 10)].
To find the displacement, we need to add these two vectors using vector addition:
Displacement vector = [(6, 0)] + [(0, 10)] = [(6, 10)]
Using the Pythagorean theorem, we can find the magnitude of the displacement vector:
Displacement = √(6^2 + 10^2) = √(36 + 100) = √136 ≈ 11.66 meters.
Now, let's calculate the difference between the distance she walked and her displacement:
Difference = Distance - Displacement = 16 meters - 11.66 meters = 4.34 meters.
Therefore, the difference between the distance she walked and her displacement is approximately 4.34 meters.
To identify the difference between the distance Benjamina walked and her displacement, let's first define these terms:
1. Distance: The total length covered by an object during its motion, regardless of direction. It is a scalar quantity and is always positive.
2. Displacement: The change in position of an object from its initial point to its final point, considering both magnitude and direction. It is a vector quantity.
Now, let's calculate the distance Benjamina walked and her displacement:
1. Distance:
Benjamina walked 6 meters to the corner of the building and then turned the corner and walked 10 meters to her friend's apartment. Therefore, the total distance she walked is:
Distance = 6 meters + 10 meters = 16 meters.
2. Displacement:
To calculate displacement, we need to determine the straight-line distance and direction from Benjamina's initial point (front door of her apartment) to her final point (her friend's apartment).
Since Benjamina walked in a rectangular path (6 meters to the corner and 10 meters along the side of the building), we can use the Pythagorean theorem to calculate the displacement:
Displacement = sqrt((6^2 + 10^2))
= sqrt(36 + 100)
= sqrt(136)
≈ 11.66 meters.
Therefore, the difference between the distance she walked and her displacement is:
16 meters - 11.66 meters ≈ 4.34 meters.