Free Fall

Free Fall

High School

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Learning Objectives

• Define free fall and identify the conditions required for it to happen.

• Explain why objects in free fall accelerate at the same rate, regardless of mass.

• Describe the velocity and acceleration changes of an object when thrown into the air.

• Use kinematic equations to solve problems about objects that are in free fall.

Key Vocabulary

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Free Fall

The motion of an object when gravity is the only significant force acting on it.

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Free-Fall Acceleration

The constant acceleration of an object due to gravity, which is 9.8 m/s² on Earth.

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Air Resistance

The force of friction that opposes an object's motion as it moves through the air.

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What is Free Fall?

• An object is in free fall when only gravity is pulling it down.

• We must ignore all other forces, including the force of air resistance.

• The object's mass and size do not affect its motion in free fall.

• This idealized motion involves the object experiencing constant downward acceleration.

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Solved Example 1
A construction worker accidentally drops a wrench from a tall building. How far does the wrench fall after 2.5 seconds, assuming it is in a state of free fall?

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Step 1: Analyze and Sketch the Problem

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Solved Example 1
A construction worker accidentally drops a wrench from a tall building. How far does the wrench fall after 2.5 seconds, assuming it is in a state of free fall?

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Step 2: Solve for the Unknown

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Solved Example 1
A construction worker accidentally drops a wrench from a tall building. How far does the wrench fall after 2.5 seconds, assuming it is in a state of free fall?

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Step 3: Evaluate the Answer

• The calculated distance is approximately 30.6 meters. The units are correct (meters), and the positive sign indicates the magnitude of the downward displacement.

• The answer is reasonable for an object falling for 2.5 seconds under gravity.

Multiple Choice

Which of the following best describes an object in a state of free fall?

• An object that is stationary in the air.

• An object that has a constant velocity.

• An object falling under the sole influence of gravity.

• An object falling with significant air resistance.

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Historical Context: A Major Misconception

Aristotle's View

• ​The Greek philosopher Aristotle believed that heavier objects fall to the ground faster than lighter ones.

• ​​This idea seemed logical based on everyday observations, like a rock falling much faster than a leaf.

• ​He concluded that an object's falling speed was directly proportional to its overall mass.

Galileo's Discovery

• ​Galileo Galilei challenged Aristotle's view through a series of careful and well-documented experiments.

• ​​He observed that objects of different masses actually reached the ground at nearly the same time.

• ​Without air resistance, he stated, all objects fall at the same rate regardless of their mass.

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Solved Example 2
A stone is dropped from a cliff and falls for 3.0 seconds. What is its final velocity, assuming no air resistance?

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Step 1: Analyze and Sketch the Problem

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Solved Example 2
A stone is dropped from a cliff and falls for 3.0 seconds. What is its final velocity, assuming no air resistance?

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Step 2: Solve for the Unknown

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Solved Example 2
A stone is dropped from a cliff and falls for 3.0 seconds. What is its final velocity, assuming no air resistance?

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Step 3: Evaluate the Answer

• The units (m/s) are correct for velocity.

• The negative sign indicates a downward direction, which is expected for a falling object. The answer is reasonable.

Multiple Choice

According to Galileo's findings, which of these would happen if a feather and a hammer were dropped from the same height in a vacuum?

• The feather would hit the ground first.

• They would hit the ground at the same time.

• They would both float and not fall.

• The hammer would hit the ground first.

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Velocity and Acceleration in Free Fall

• An object in free fall has a constant downward acceleration of -9.8 m/s².

• When moving up, velocity is positive but decreases, so the object slows down.

• At its peak, the object's velocity is 0 m/s, but acceleration remains -9.8 m/s².

• While falling, velocity is negative and its magnitude increases, so the object speeds up.

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Solved Example 3
A ball is thrown straight up, reaching a maximum height of 5.0 meters. At what initial velocity was it thrown? (Use g = -9.8 m/s²)

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Step 1: Analyze and Sketch the Problem

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Solved Example 3
A ball is thrown straight up, reaching a maximum height of 5.0 meters. At what initial velocity was it thrown? (Use g = -9.8 m/s²)

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Step 2: Solve for the Unknown

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Solved Example 3
A ball is thrown straight up, reaching a maximum height of 5.0 meters. At what initial velocity was it thrown? (Use g = -9.8 m/s²)

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Step 3: Evaluate the Answer

• The calculated velocity is approximately 9.9 m/s, and the positive sign is correct for an initial upward throw.

• The magnitude is reasonable for achieving a height of 5 meters, so the answer makes physical sense.

Multiple Choice

What are the velocity and acceleration of a ball at the very top of its path when thrown vertically upward?

• Velocity is 0 m/s, and acceleration is -9.8 m/s²

• Velocity is 0 m/s, and acceleration is 0 m/s²

• Velocity is positive, and acceleration is -9.8 m/s²

• Velocity is negative, and acceleration is 0 m/s²

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Analyzing Free Fall Motion

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Solved Example 4
A ball is thrown straight up with an initial velocity of 15 m/s. How high will the ball go before it starts to fall back down? (Neglect air resistance).

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Step 1: Analyze and Sketch the Problem

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Solved Example 4
A ball is thrown straight up with an initial velocity of 15 m/s. How high will the ball go before it starts to fall back down? (Neglect air resistance).

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Step 2: Solve for the Unknown

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Solved Example 4
A ball is thrown straight up with an initial velocity of 15 m/s. How high will the ball go before it starts to fall back down? (Neglect air resistance).

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Step 3: Evaluate the Answer

Multiple Choice

A coaster starts from rest and is in free fall for 1.5 seconds. Using the formula v_f = v_i + gt, what is its velocity at this time? (Use g = -9.8 m/s²)

• 14.7 m/s

• -11.0 m/s

• -9.8 m/s

• -14.7 m/s

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Common Misconceptions About Free Fall

Misconception	Correction
Heavier objects fall faster than lighter ones.	In a vacuum, all objects fall with the same acceleration.
At its peak, a thrown object has zero acceleration.	Acceleration is always -9.8 m/s2 during free fall.
An object in free fall has a constant velocity.	An object in free fall constantly accelerates, so its velocity changes.

Multiple Choice

How does the motion of a bowling ball and a marble compare if both are dropped from the same height in a vacuum?

• The bowling ball will accelerate faster because it has more mass.

• They will fall with different accelerations but have the same displacement.

• The marble will accelerate faster because it has less air resistance.

• They will have the same acceleration and hit the ground at the same time.

Multiple Choice

Why does a ball thrown vertically into the air slow down as it rises?

• Air resistance pushes the ball downward.

• The force of the throw wears off as it gets higher.

• Its velocity is upward (positive) while its acceleration is downward (negative).

• Its acceleration becomes positive on the way up.

Multiple Choice

An astronaut on the Moon, where there is no air, drops a hammer and a feather from the same height. What outcome supports the principles of free fall?

• The hammer will land first because it is heavier.

• Both objects will hit the lunar surface simultaneously.

• The feather will land first because it is lighter.

• The objects will float away because there is less gravity.

Multiple Choice

A stone is dropped from a cliff. If it takes 3 seconds to hit the ground, what is its approximate final velocity just before impact, assuming no air resistance? (Use g ≈ 10 m/s²)

• -10 m/s

• -15 m/s

• -20 m/s

• -30 m/s

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Summary

Poll

On a scale of 1-4, how confident are you about solving free fall problems?

• 1

• 2

• 3

• 4