Vertical Motion Under Gravity

Active learning works here because students often hold onto intuitive but incomplete ideas about motion and forces. Moving, drawing, and discussing forces in real time helps them confront and revise these ideas. This topic benefits from concrete, hands-on experiences to make abstract concepts visible and memorable.

• Year 12
• Mathematics
• 3 activities
• 20 min–45 min

Learning Objectives

1. Calculate the maximum height reached by an object thrown vertically upwards.
2. Determine the total time of flight for an object launched and landing at the same vertical level.
3. Analyze the symmetry of an object's vertical motion under gravity, comparing its upward and downward journeys.
4. Construct solutions to problems involving objects projected vertically under constant gravitational acceleration, neglecting air resistance.

Inquiry Circle

⏱ 45 min·Small Groups

Inquiry Circle: The Tug-of-War Vector

Using force meters, students pull on a central ring from three different directions. They must record the forces and use vector addition (drawing or trigonometry) to show that the resultant force is zero when the ring is stationary.

Prepare & details

Analyze the symmetry of vertical motion under gravity.

Facilitation Tip: During the Tug-of-War Vector, place students in small groups and require each to sketch a force diagram before sharing with the class to build consensus on balanced forces.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Simulation Game

⏱ 40 min·Small Groups

Station Rotations: Free Body Diagram Clinic

Set up stations with physical setups (e.g., a block on a ramp, a weight hanging from a pulley). Students must draw the Free Body Diagram for each, identifying all forces and their directions before moving to the next station.

Prepare & details

Construct solutions for projectile motion problems neglecting air resistance.

Facilitation Tip: In the Free Body Diagram Clinic, circulate and ask each group to explain why their diagram matches the scenario, not just what they drew.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Think-Pair-Share

⏱ 20 min·Pairs

Think-Pair-Share: Newton's Third Law Paradox

Present the classic 'Horse and Cart' problem: if the horse pulls the cart and the cart pulls back with an equal force, how does anything move? Students discuss in pairs and then explain the answer to the class.

Prepare & details

Predict the maximum height and time of flight for an object thrown vertically.

Facilitation Tip: For the Newton’s Third Law Paradox, assign roles so each pair debates a different paradox before switching to ensure all students engage with the counter-intuitive ideas.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Teaching This Topic

Teaching this topic successfully means balancing conceptual understanding with procedural fluency. Avoid rushing to calculations before students grasp the physical meaning of forces. Use everyday examples like tug-of-war or objects on slopes to anchor abstract ideas. Research suggests that students benefit from repeated exposure to vector diagrams, so integrate them in multiple contexts. Always link back to Newton’s laws to reinforce the ‘why’ behind motion.

What to Expect

By the end of these activities, students will confidently explain motion using Newton’s laws, draw and interpret vector diagrams, and resolve forces in different contexts. They will move from describing motion to explaining its causes with precision and clarity.

Watch Out for These Misconceptions

Common Misconception

During the Collaborative Investigation: The Tug-of-War Vector, watch for students who assume the winning side applies a larger force. Redirect them by asking them to measure the rope’s tension and relate it to balanced forces.

What to Teach Instead

During the Collaborative Investigation: The Tug-of-War Vector, ask students to use spring scales to measure the tension on both sides. If both read the same value, emphasize that the forces are balanced even if one team moves, reinforcing Newton’s First Law.

Common Misconception

During the Station Rotations: Free Body Diagram Clinic, watch for students who draw the normal force equal to mg on an incline. Redirect them by having them measure and compare the normal force to the vertical component of weight.

What to Teach Instead

During the Station Rotations: Free Body Diagram Clinic, provide blocks and a protractor at the slope station. Ask students to measure the angle and calculate the normal force using mg cosθ, showing that it is not always equal to mg.

Assessment Ideas

Quick Check

After the Collaborative Investigation: The Tug-of-War Vector, present students with a vertical motion scenario: a 0.5 kg ball thrown upward at 20 m/s. Ask them to calculate the velocity after 1.5 seconds and the maximum height, observing their use of SUVAT equations and correct sign conventions for acceleration.

Exit Ticket

During the Think-Pair-Share: Newton’s Third Law Paradox, ask students to write a brief explanation on a slip of paper: Describe why the force the Earth exerts on you is equal to the force you exert on the Earth, even though the Earth doesn’t move. Evaluate their understanding of action-reaction pairs and symmetry.

Discussion Prompt

After the Station Rotations: Free Body Diagram Clinic, pose the question: How would the maximum height and time of flight of a projectile change if we considered air resistance? Facilitate a class discussion on the limitations of the idealized model and introduce factors like drag and terminal velocity.

Extensions & Scaffolding

• Challenge students to design a real-world scenario where Newton’s Third Law is counterintuitive and explain it using a vector diagram.
• For students struggling with inclined planes, provide pre-drawn diagrams with labeled components and ask them to relate the angles to the weight vector.
• Deeper exploration: Have students research and present on how engineers account for friction and air resistance in designing safety features like seatbelts or parachutes.

Key Vocabulary

SUVAT equations	A set of five kinematic equations that describe motion with constant acceleration, relating displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).
Gravitational acceleration (g)	The constant acceleration experienced by an object due to Earth's gravity, approximately 9.8 m/s², directed downwards.
Maximum height	The highest vertical position an object reaches during its trajectory, occurring when its vertical velocity momentarily becomes zero.
Time of flight	The total duration an object spends in the air, from the moment it is projected until it returns to its starting vertical level.
Displacement	The change in position of an object, a vector quantity representing the shortest distance from the initial to the final position.