Physics · 10th Grade · Kinematics: The Mathematics of Motion · Weeks 1-9

Free Fall and Gravity

Investigating the motion of objects influenced solely by gravity. Students calculate time, height, and velocity for objects dropped or thrown vertically.

• Common Core State Standards
• STD.HS-PS2-1
• STD.HS-ESS1-4

About This Topic

Free fall is the case of pure gravitational acceleration with no other forces acting. Near Earth's surface, all objects accelerate downward at 9.8 m/s² regardless of mass, a result that surprises many students but follows directly from Newton's second law when gravitational force scales proportionally with mass. This topic connects to both NGSS HS-PS2-1 and HS-ESS1-4, linking terrestrial mechanics to gravitational interactions across the solar system.

Students apply the kinematic equations to vertical motion, calculating drop times, maximum heights, and impact velocities. The classic 'dropped vs. thrown horizontally' demonstration, or the virtual equivalent, establishes that vertical and horizontal motions are independent, previewing projectile motion. Air resistance is introduced as a real-world deviation from the ideal model, explaining terminal velocity and parachute design.

Active learning is productive here because free fall carries strong prior misconceptions (heavier objects fall faster) that direct instruction alone rarely corrects. Prediction-observation-explanation sequences, where students commit to a prediction before watching a feather-and-coin drop in vacuum, create the cognitive dissonance that makes the correct concept stick.

Key Questions

1. Why do all objects fall at the same rate in a vacuum regardless of mass?
2. How does air resistance change the ideal model of free fall in the real world?
3. How would your hang-time on a basketball jump differ on the Moon?

Learning Objectives

• Calculate the time of flight, maximum height, and final velocity of an object dropped from rest using kinematic equations.
• Compare the theoretical free fall motion of objects in a vacuum with their motion in the presence of air resistance.
• Explain why objects of different masses fall at the same rate in a vacuum, referencing Newton's second law and the law of universal gravitation.
• Analyze how changes in gravitational acceleration, such as on the Moon, would affect the vertical motion of an object.

Before You Start

Introduction to Kinematics: Displacement, Velocity, and Acceleration

Why: Students need a foundational understanding of these basic kinematic variables and their relationships to solve problems involving motion.

Newton's Laws of Motion

Why: Understanding Newton's second law (F=ma) is crucial for comprehending why objects accelerate at the same rate in a vacuum under gravity.

Key Vocabulary

Free Fall	The motion of an object where gravity is the only force acting upon it. Air resistance is ignored in this idealized model.
Acceleration due to gravity (g)	The constant rate at which objects accelerate towards Earth's center, approximately 9.8 m/s², regardless of their mass or composition.
Air Resistance	A type of friction that opposes the motion of an object through the air, dependent on factors like speed, shape, and surface area.
Terminal Velocity	The constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration.

Watch Out for These Misconceptions

Common Misconception

Heavier objects fall faster than lighter ones.

What to Teach Instead

In a vacuum, all objects fall at the same rate because gravitational force increases proportionally with mass, so the extra force is exactly offset by the extra inertia. Air resistance causes different fall rates in everyday experience, which students often over-generalize. The vacuum drop demonstration is the most direct fix.

Common Misconception

A thrown object has a 'force of the throw' acting on it while in the air.

What to Teach Instead

Once released, the only force on a projectile (ignoring air resistance) is gravity. The initial velocity given by the throw is a starting condition, not an ongoing force. Asking students to draw force diagrams at several points mid-flight helps them identify that the throw's effect is already encoded in the initial velocity.

Common Misconception

Objects stop accelerating when they reach maximum height.

What to Teach Instead

At the peak of a vertical throw, velocity is zero but acceleration is still 9.8 m/s² downward. Students often confuse zero velocity with zero acceleration. Position-velocity-acceleration graphs on the same time axis clarify that acceleration is constant throughout the flight.

Active Learning Ideas

Predict-Observe-Explain: Vacuum Drop Demo

Students write individual predictions about whether a feather or coin will hit the ground first, then observe a vacuum-tube drop (video or live). They explain in writing why the result contradicts mass-dependent intuition, then share explanations with a partner to refine their reasoning.

20 min·Individual

Inquiry Circle: Free Fall Timer

Groups drop measured objects from a fixed height and use slow-motion phone video to measure fall time. They calculate g from their data, compare to 9.8 m/s², and discuss sources of discrepancy including reaction time and air resistance on lighter objects.

45 min·Small Groups

Think-Pair-Share: Moon Jump Hang Time

Present students with the scenario of a basketball player jumping on the Moon with the same leg force as on Earth. Students individually calculate hang time, then pair to check each other's equations, and share with the class why only gravitational acceleration changes the answer.

25 min·Pairs

Gallery Walk: Air Resistance Cases

Post four station boards showing different falling objects (feather, golf ball, skydiver, raindrop). Student pairs sketch velocity-time graphs for each, label where terminal velocity is reached, and explain the force balance at that point before rotating to the next station.

30 min·Pairs

Real-World Connections

• Skydivers must understand air resistance and terminal velocity to safely deploy their parachutes. The design of parachutes is critical for slowing their descent to a manageable landing speed.
• Engineers designing satellites and spacecraft must account for gravitational forces and acceleration. Understanding free fall principles is essential for calculating orbital trajectories and reentry paths.
• Athletes in sports like basketball or high jump utilize principles of vertical motion and gravity. Analyzing hang time involves calculating the duration an object (or person) is in the air under gravitational influence.

Assessment Ideas

Quick Check

Present students with a scenario: 'An object is dropped from a height of 50 meters. Calculate how long it will take to hit the ground and its velocity just before impact.' Have students show their work using the kinematic equations.

Discussion Prompt

Pose the question: 'Imagine dropping a feather and a bowling ball simultaneously in a vacuum chamber. What would happen, and why? Now, consider dropping them in a regular classroom. How would the outcome differ, and what force causes this difference?'

Exit Ticket

Ask students to write down two key differences between free fall in a vacuum and free fall with air resistance. For each difference, provide a brief explanation.

Frequently Asked Questions

Why do all objects fall at the same rate in a vacuum?

Gravitational force on an object equals its mass times g (F = mg). Newton's second law gives acceleration as F/m, so the mass cancels out and every object gets the same acceleration. The catch is that air resistance adds a force that depends on shape and size, not mass, so in air, objects fall at different rates.

How does air resistance change free fall in the real world?

Air resistance is a drag force opposing motion that grows with speed. As an object accelerates downward, drag increases until it equals gravitational force. At that point net force is zero, acceleration stops, and the object falls at constant 'terminal velocity.' A skydiver and a styrofoam ball reach very different terminal velocities despite falling in the same gravitational field.

How would hang time on a basketball jump differ on the Moon?

The Moon's surface gravity is about 1.62 m/s², roughly one-sixth of Earth's. Using the hang-time formula (t = 2v₀/g), the same initial upward velocity produces about six times the hang time on the Moon. A player who gets 0.5 s of air time on Earth would get roughly 3 seconds on the Moon.

How does active learning improve understanding of free fall?

Free fall carries stubborn misconceptions, particularly that mass determines fall rate, that survive passive instruction. Prediction-Observe-Explain sequences force students to commit to a wrong prediction, observe the contradiction, and reconstruct their understanding. That cognitive conflict, created by their own prediction, is far more effective than simply being told the correct answer.