Math Problem Statement
The walking and measuring distance exercise, including turning 180 degrees and calculating displacement.
Solution
Based on the image you provided, here's a breakdown of the walking exercise involving the vectors and measurements:
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Initial Setup (Origin): Place a cone where you begin. This is your origin.
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Step b:
- Walk 4 steps forward, then place a cone.
- Distance walked: 2.7 m.
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Step c:
- Turn around (180 degrees) and walk 2 steps.
- Distance walked: 1.3 m.
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Step d:
- Turn 180 degrees again and walk 4 steps.
- Distance walked: 2.45 m.
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Step e:
- Measure your displacement from the origin.
- Measured displacement: 3.9 m.
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Step f:
- Draw vector arrows representing each movement and label them with their respective distances (2.7 m, 1.3 m, and 2.45 m), adding vectors head-to-tail.
Further Questions
- How do you determine the direction of the vectors when drawing them?
- What is the importance of turning 180 degrees in step c?
- How does the measured displacement compare with the sum of individual distances walked?
- How can vectors be added graphically using the head-to-tail method?
- What is the difference between total distance walked and displacement?
Tip:
When calculating displacement, consider both the magnitude and direction of each movement, as displacement is a vector quantity that depends on the overall change in position from the origin.
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Math Problem Analysis
Mathematical Concepts
Vector Addition
Displacement
Distance Measurement
Formulas
Displacement = final position - initial position
Theorems
Pythagorean Theorem (if applicable for vector calculation)
Suitable Grade Level
Grades 6-9