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:

  1. Initial Setup (Origin): Place a cone where you begin. This is your origin.

  2. Step b:

    • Walk 4 steps forward, then place a cone.
    • Distance walked: 2.7 m.
  3. Step c:

    • Turn around (180 degrees) and walk 2 steps.
    • Distance walked: 1.3 m.
  4. Step d:

    • Turn 180 degrees again and walk 4 steps.
    • Distance walked: 2.45 m.
  5. Step e:

    • Measure your displacement from the origin.
    • Measured displacement: 3.9 m.
  6. 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

  1. How do you determine the direction of the vectors when drawing them?
  2. What is the importance of turning 180 degrees in step c?
  3. How does the measured displacement compare with the sum of individual distances walked?
  4. How can vectors be added graphically using the head-to-tail method?
  5. 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