A shopper pushes a cart 40 m south down one aisle and then turns 90.0° west and moves 18 m. He then makes another 90.0° turn and moves 17 m
What is the largest possible displacement of the shopper? couterclockwise west
What is the smallest possible displacement of the shopper? couterclockwise west
where do i even begin?
Take a piece of paper, draw some isles (north-south).
Designate a starting point of the shopper.
Follow the directions:
40 m. down one aisle towards south.
turn west and move 18 m. (about 3 aisles).
Turn north OR south and move 17 m.
Based on the initial position, and each of the final positions, calculate the displacement of the shopper.
Displacement is defined as the difference between the final and initial positions, both in distance and in direction.
Post if you could use more help, and say where the problem is.
OHhh that makes much more since. I thought you could only go 17m one way. Thanks I figured it out.
You're welcome!
Do you mind explaining this fully?
To find the largest and smallest possible displacements of the shopper, we need to break down their movements into components and then use vector addition.
1. First, let's break down the shopper's movements into two parts:
- In the first part, the shopper moves 40 m south. This can be represented as a displacement of (-40 m, 0 m).
- In the second part, the shopper turns 90.0° west and moves 18 m. This can be represented as a displacement of (0 m, -18 m).
2. Now, let's add the two displacements to find the total displacement of the shopper:
- For the largest possible displacement, we assume that the shopper's second turn is counter-clockwise, which means they turn to the left. In this case, the two displacements are in opposite directions. So, to find the total displacement, we need to subtract one from the other.
Total displacement for largest: (-40 m, 0 m) - (0 m, -18 m)
= (-40 m, 18 m)
- For the smallest possible displacement, we assume that the shopper's second turn is clockwise, which means they turn to the right. In this case, the two displacements are in the same direction. So, to find the total displacement, we need to add them together.
Total displacement for smallest: (-40 m, 0 m) + (0 m, -18 m)
= (-40 m, -18 m)
3. Finally, we can find the magnitude (or length) of each displacement using the Pythagorean theorem:
- Magnitude of the largest displacement:
|(-40 m, 18 m)| = √((-40)^2 + 18^2) = √(1600 + 324) = √1924 ≈ 43.88 m
- Magnitude of the smallest displacement:
|(-40 m, -18 m)| = √((-40)^2 + (-18)^2) = √(1600 + 324) = √1924 ≈ 43.88 m
So, both the largest and smallest possible displacements of the shopper are approximately 43.88 meters in the counter-clockwise west direction.