• DISPLACEMENT (Δx)

• Remember: "rate" means "per unit time".
• Velocity is a vector quantity and is measured in m.s^-1. 
• Average velocity is calculated using the following equation:

• 𝒗_𝒂𝒗 = ∆𝒙 / ∆𝑡

Challenge: You’ll be navigators on a treasure hunt!

Objective: Navigate the school field using vectors to find hidden treasure, applying vector addition and direction.

Duration: 20 minutes

Materials Needed (per team):

• Measuring tape

• Compass (for direction)

• Graph paper and pencil

• Calculator

Team Roles:

• Navigator: Uses the compass to find direction.

• Measurer: Measures distances with the tape.

• Recorder: Notes observations and calculations.

Instructions for Students

Step 1: Understand Your Mission (2 minutes)

• Your team has vectors leading to a hidden treasure (marked by a flag).

• Starting point: Center of the rugby field

• Goal: Follow the vectors to find the treasure by navigating and sketching.

Step 2: Plot Vectors on Graph Paper (5 minutes)

• Use graph paper with a scale: 1 cm = 1 m.

• Draw the vectors head-to-tail:

1. Start at (0,0).

2. Use the compass to measure direction (0° = due North, bearing 90 = due East)

3. Draw each vector’s length (magnitude).

• Estimate the treasure’s location by connecting the vectors.

Step 3: Navigate to the Treasure (10 minutes)

• Go to the starting point (rugby field center).

• Follow each vector using the compass (Navigator) and measuring tape (Measurer):

1. Move in the direction and distance of Vector 1.

2. From there, move in the direction and distance of Vector 2, etc.

• Recorder: Note landmarks or observations.

• Find the treasure (flag) and confirm its code with your teacher.

Group 1: Two Vectors to Resultant

• Vectors:

  1. Vector 1: 6 m at 30° (30° east of north)

  2. Vector 2: 4 m at 0° (due north)

• Task:

  1. Sketch vectors head-to-tail on graph paper (1 cm = 1 m).

  2. Navigate to the treasure by following the vectors.

  3. Estimate the resultant displacement (magnitude and bearing) by measuring your sketch.

Group 2: Two Vectors to Resultant

• Vectors:

  1. Vector 1: 5 m at 45° (45° east of north)

  2. Vector 2: 3 m at 270° (due west)

• Task:

  1. Sketch vectors head-to-tail.

  2. Navigate to the treasure.

  3. Estimate the resultant displacement on your sketch.

Group 3: Three Vectors to Resultant

• Vectors:

  1. Vector 1: 4 m at 90° (due east)

  2. Vector 2: 5 m at 30° (30° east of north)

  3. Vector 3: 3 m at 180° (due south)

• Task:

  1. Sketch vectors head-to-tail.

  2. Navigate to the treasure.

  3. Estimate the resultant displacement on your sketch.

Group 4: Three Vectors to Resultant

• Vectors:

  1. Vector 1: 7 m at 315° (45° west of north)

  2. Vector 2: 4 m at 0° (due north)

  3. Vector 3: 2 m at 270° (due west)

• Task:

  1. Sketch vectors head-to-tail.

  2. Navigate to the treasure.

  3. Estimate the resultant displacement on your sketch.

Group 5: Resultant to Component Vectors

• Resultant: 7 m at 45° (45° east of north)

• Task:

  1. Sketch the resultant vector on graph paper.

  2. Propose two component vectors that, when added head-to-tail, give the resultant (e.g., one due north, one due east).

  3. Navigate to the treasure using the resultant vector.

  4. Verify your component vectors by navigating their path to the same treasure.

• Hint: Possible components: 4.95 m at 0° (north), 4.95 m at 90° (east).

Calculation and Sketch

• Sketch: Draw vectors head-to-tail (Groups 1–4) or resultant and components (Group 5). Label all vectors.

• Quick Check: For Groups 1–4, estimate the resultant (magnitude and bearing) from your sketch. For Group 5, list your two component vectors and show they produce the resultant.
  [Space for sketch and notes]

Reflection Question

1. How did the head-to-tail method help you navigate? What was the biggest challenge using bearings (0° = north, 90° = east)?