Unit 1 · Lesson 3c

3cFree Fall and Gravity

Discover why all objects fall at the same rate, apply g = 9.8 m/s² to solve free-fall problems, and understand terminal velocity.

Free fall is the purest example of constant acceleration. Mastering it builds intuition for all projectile motion and lays the groundwork for understanding gravitational force in Newton's laws.

Lesson Overview

Free fall is the motion of an object under the sole influence of gravity, with no air resistance. In this lesson you will learn that all objects fall with the same constant acceleration g = 9.8 m/s² downward, apply the kinematic equations to free-fall problems, and explore terminal velocity as a real-world modification of ideal free fall.

Key Concepts

Free Fall Definition

Motion under gravity alone — no air resistance, no other forces acting

g = 9.8 m/s² Downward

The acceleration due to gravity near Earth's surface; always directed downward

Mass Independence

All objects fall at the same rate regardless of mass (Galileo's principle)

Sign Convention

Taking downward as negative: a = −9.8 m/s²; taking downward as positive: a = +9.8 m/s²

Objects Thrown Upward

Still experience g downward; velocity decreases going up, increases coming down

Terminal Velocity

Maximum speed reached when air resistance equals gravitational force; free fall ends

Example 1

A ball is dropped from rest from a height of 45 m. How long does it take to hit the ground? (Take downward as positive, g = 9.8 m/s²)

Answer:Known: v₀ = 0, a = 9.8 m/s², x = 45 m. Use x = v₀t + ½at² → 45 = ½(9.8)t² → t² = 9.18 → t ≈ 3.03 s.
Example 2

A stone is dropped from a bridge. What is its velocity after 4 s of free fall?

Answer:v = v₀ + at = 0 + (9.8)(4) = 39.2 m/s downward.
Example 3

A ball is thrown upward at 20 m/s. How high does it rise before stopping? (Take upward as positive, a = −9.8 m/s²)

Answer:Known: v₀ = 20 m/s, v = 0, a = −9.8 m/s². Use v² = v₀² + 2ax → 0 = 400 + 2(−9.8)x → x = 400/19.6 ≈ 20.4 m.
Example 4

A ball is thrown upward at 15 m/s. How long does it take to return to the thrower's hand?

Answer:Time to reach peak: v = v₀ + at → 0 = 15 − 9.8t → t = 1.53 s. Total time = 2 × 1.53 ≈ 3.06 s (symmetric flight).
Example 5

A feather and a hammer are dropped simultaneously on the Moon (no atmosphere). Which hits the ground first?

Answer:Both hit at the same time. Without air resistance, all objects fall with the same acceleration regardless of mass — as demonstrated by Apollo 15 astronaut David Scott.

External Supplemental Resource

Guided Practice Video: Free Fall and Gravity

Review free fall, g = 9.8 m/s², and worked problems for objects dropped or thrown vertically before completing the guided practice problems below.

Video by The Organic Chemistry Tutor on YouTube

Watch on YouTube ↗
Guided Problem 1

A rock is dropped from a cliff 80 m high. How long does it take to reach the bottom?

Hint: Use x = ½gt² with g = 9.8 m/s² and x = 80 m. Solve for t.

Guided Problem 2

A ball is thrown upward at 25 m/s. What is its velocity 3 s later?

Hint: Use v = v₀ + at with a = −9.8 m/s² (upward positive). The sign of the answer tells you the direction.

Guided Problem 3

An object in free fall reaches a speed of 29.4 m/s. How long has it been falling?

Hint: Use v = gt (starting from rest). Divide the final speed by g.

Guided Problem 4

A skydiver reaches terminal velocity of 55 m/s. What does this tell you about the forces acting on her?

Hint: At terminal velocity, acceleration = 0. What must be true about the net force?

Guided Problem 5

A ball is thrown upward at 12 m/s from the edge of a 30 m cliff. How long does it take to hit the ground at the base of the cliff? (Take upward as positive)

Hint: Set up x = v₀t + ½at² with x = −30 m (ground is 30 m below launch point). Solve the quadratic for t > 0.

Key Vocabulary

Free Fall

The motion of an object subject only to the force of gravity, with no air resistance.

Example: A ball dropped in a vacuum tube is in true free fall.

Acceleration Due to Gravity (g)

The constant downward acceleration of 9.8 m/s² experienced by all freely falling objects near Earth's surface.

Example: A dropped ball gains 9.8 m/s of downward speed every second.

Terminal Velocity

The constant maximum speed reached when air resistance equals the gravitational force, resulting in zero net force and zero acceleration.

Example: A skydiver reaches terminal velocity of about 55 m/s in a spread-eagle position.

Projectile

Any object that is launched and then moves under the influence of gravity alone (ignoring air resistance).

Example: A thrown ball, a fired bullet, and a cliff-diver are all projectiles.

Interactive Practice — 5 Questions

1

What is the acceleration due to gravity near Earth's surface?

2

A ball is dropped from rest. What is its speed after 3 s of free fall?

3

A 1 kg ball and a 5 kg ball are dropped simultaneously from the same height in a vacuum. Which hits the ground first?

4

At terminal velocity, the net force on a falling object is:

5

A ball thrown upward at 19.6 m/s reaches its peak after:

Independent Practice

1

A stone is dropped from a 122.5 m tower. Find (a) the time to reach the ground and (b) the speed just before impact.

2

A ball is thrown upward at 30 m/s. Find (a) the maximum height, (b) the time to reach the peak, and (c) the total time in the air.

3

Explain in your own words why a heavy rock and a light feather fall at the same rate in a vacuum but not in air.

4

A skydiver jumps from a plane. Describe how her acceleration changes from the moment she jumps until she reaches terminal velocity.

5

★ A ball is thrown upward at 14 m/s from the top of a 20 m building. Find the total time until it hits the ground and its speed at impact. (Take upward as positive, a = −9.8 m/s²)

Challenge
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Common Mistakes

Thinking that heavier objects fall faster than lighter ones.

In the absence of air resistance, all objects fall with the same acceleration g = 9.8 m/s², regardless of mass.

Setting acceleration to zero at the peak of a thrown object's path.

Velocity is zero at the peak, but acceleration is still g = 9.8 m/s² downward throughout the entire flight.

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Math Tips

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Choose a consistent sign convention at the start of every free-fall problem. If upward is positive, then a = −9.8 m/s² always. Write this at the top of your work and never switch mid-problem.