Module 1 · Lesson

Relative Motion

Kinematics

Relative Motion

Orientation

Lesson goal: build accurate physics fluency for relative motion and use that fluency to support clear HSC-style scientific writing.

This page is materialised into the MentorMind course shell from existing teaching, textbook, and eduKG material. Use it as the main lesson surface; use the tutor for targeted repair, worked examples, and concise writing feedback.

Source Lesson Material

Syllabus inquiry question

From The Feynman Lectures on Physics, Vol I, Chapter 15:

Motion is always measured relative to a chosen frame. Changing the frame changes the numbers, but it does not change the physics.

Learning Objectives

Content

Relative velocity in one dimension

Relative velocity compares two objects moving along the same line:

$$v_{AB} = v_A - v_B$$

This reads as "the velocity of A relative to B".

$v_{AB}$ means "velocity of A as observed from B" or "velocity of A relative to B"

Interactive: One-Dimensional Relative Motion

Consider two cars on a highway. Their relative velocity determines how quickly the gap between them changes.

Example: Car A at 25 m/s, Car B at 18 m/s (both east)

Relative velocity in two dimensions

Vectors are subtracted component-wise. The relative velocity points from the observer to the object being described.

$$\vec{v}_{AB} = \vec{v}_A - \vec{v}_B$$

Interactive: Boat and River Current

A classic relative motion problem: a boat crossing a river with current.

Interpreting the diagram:

Reference frames

A statement about motion is incomplete without a frame. The same motion can be described differently in different frames without contradiction.

All velocity measurements require specifying:

  1. What is moving
  2. Relative to what it's being measured

Common Relative Motion Scenarios

ScenarioFrame AFrame BRelative Velocity
Overtaking carsGroundSlower carDifference in speeds
Boat in currentWaterGroundVector sum
Rain on cyclistGroundCyclistVector difference
Aircraft in windAirGroundVector sum

Worked Examples

Example 1: Overtaking cars

Car A travels at 25 m/s east. Car B travels at 18 m/s east. Find A relative to B.

Solution:

  1. $v_{AB} = v_A - v_B = 25 - 18 = 7$ m/s
  2. The positive result indicates A moves east relative to B
  3. A closes the gap at 7 m/s

Example 2: Boat and current

A boat heads due north at 4.0 m/s relative to the water. The current is 1.5 m/s east. Find velocity relative to the ground.

Solution:

  1. Components: $v_x = 1.5$ m/s, $v_y = 4.0$ m/s
  2. Speed: $\sqrt{1.5^2 + 4.0^2} = \sqrt{18.25} = 4.3$ m/s
  3. Direction: $\tan^{-1}(1.5/4.0) = 20 degrees$ east of north

Example 3: Rain and a moving cyclist

Rain falls vertically at 6.0 m/s. A cyclist rides east at 5.0 m/s. Find the rain velocity relative to the cyclist.

Solution:

The rain's velocity relative to the cyclist is found by vector subtraction:

$$\vec{v}{rain/cyclist} = \vec{v}{rain} - \vec{v}_{cyclist}$$

  1. Rain (relative to ground): $v_x = 0$, $v_y = -6.0$ m/s (downward)
  2. Cyclist (relative to ground): $v_x = 5.0$ m/s, $v_y = 0$
  3. Rain relative to cyclist: $v_x = 0 - 5.0 = -5.0$ m/s, $v_y = -6.0$ m/s

Result:

The rain appears to come from ahead! This is why cyclists lean forward in rain.

Example 4: Head-on collision approach

Two trains approach each other. Train A travels at 30 m/s east, Train B at 25 m/s west.

Solution:

Taking east as positive:

Relative velocity:

The trains approach each other at the sum of their speeds.

Interactive: Aircraft Navigation

An aircraft must aim off-course to compensate for wind:

Navigation problem: To fly due north (90 degrees), the pilot must aim slightly west to compensate for the eastward wind.

Common Misconceptions

Practice Questions

Easy (2 marks)

A bus moves at 12 m/s east. A passenger walks at 1.5 m/s east relative to the bus. Find the passenger's speed relative to the ground.

Answer: $v_{pg} = v_{pb} + v_{bg} = 1.5 + 12 = 13.5$ m/s east

Medium (4 marks)

A swimmer aims straight across a river at 1.8 m/s relative to the water. The current flows 1.2 m/s downstream. Find the swimmer's ground velocity and direction.

Answer:

Hard (5 marks)

Plane A flies 250 km/h north. Plane B flies 180 km/h east. Determine the velocity of A relative to B.

Solution:

$\vec{v}_{AB} = \vec{v}_A - \vec{v}_B$

Components:

Relative speed:

Direction:

Answer: 308 km/h at 36 degrees west of north

From B's perspective, A appears to move northwest.

Multiple Choice Questions

Test your understanding with these interactive questions:

Summary

Self-Assessment

Check your understanding:

After studying this section, you should be able to:

Module 1 Complete

Congratulations on completing Module 1: Kinematics!

Scientific Writing And Exam Support

When answering questions from this lesson, separate:

For explanation questions, write in the pattern: claim -> physics reason -> consequence. For calculation questions, state the formula, substitute with units, calculate, then interpret the answer.

Tutor Context

Use this lesson context when the student asks about relative motion, related calculations, representations, or scientific writing. Prefer a short diagnostic before re-teaching. Check whether the student is confusing closely related categories such as force, velocity, acceleration, field, energy, momentum, model evidence, or mathematical representation.

Useful tutor diagnostic:

Which quantity is changing here, what causes that change, and what unit should the final answer use?

Maintenance Loop

One-minute retrieval:

  1. State the key law, model, or relationship used in this lesson.
  2. Identify one common misconception that would lead to a wrong answer.
  3. Write one sentence that links the calculation or evidence back to the physical meaning.

Source Trace

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