Free Fall Physics: Motion in One Dimension Worksheet Solutions

In the realm of physics, understanding the mechanics of free fall is crucial for students and enthusiasts alike. Free fall describes the motion of objects under the sole influence of gravity, ignoring the effects of air resistance. This principle not only forms the foundation of classical mechanics but also finds applications in everyday life, from calculating the descent of an apple from a tree to more complex scenarios involving spacecraft re-entry.

What is Free Fall?

Free fall refers to the movement of an object when gravity is the only force acting upon it. On Earth, this means:

• The acceleration due to gravity (denoted as g) is approximately 9.8 meters per second squared (m/s²).
• Objects fall towards the Earth regardless of their mass at the same rate, as demonstrated by experiments like those of Galileo Galilei.

Free Fall Equations

The following equations are fundamental in describing one-dimensional motion under the influence of gravity:

• Velocity Equation: ( v = u + at ), where:
  • v = final velocity
  • u = initial velocity
  • a = acceleration due to gravity (g for Earth)
  • t = time
• Distance Equation: ( s = ut + \frac{1}{2}at^2 ), where:
  • s = displacement
  • Other terms are as described above.

Worksheet Solutions

Problem 1: Simple Fall

A ball is dropped from a height of 20 meters. Calculate:

1. The time it takes to hit the ground.
2. The velocity when it hits the ground.

Given:

• Initial velocity u = 0 m/s
• Distance s = 20 m
• Acceleration g = 9.8 m/s²

Solution for Time:

We use the distance equation, solving for time:

s = 0 + (1/2) * 9.8 * t²
t² = (2 * s) / g
t = √((2 * 20) / 9.8) = √(40 / 9.8) ≈ 2.02 s

Solution for Velocity:

Using the velocity equation:

v = 0 + 9.8 * 2.02 ≈ 19.8 m/s

⏳ Note: Ensure units are consistent for accurate calculation.

Problem 2: Thrown Upwards

A stone is thrown vertically upwards with an initial speed of 30 m/s. Calculate:

1. The maximum height it reaches.
2. The time it takes to reach the maximum height.

Solution for Maximum Height:

At the top of its trajectory, the velocity is zero:

v² = u² + 2as
0 = (30)² + 2 * (-9.8) * h
h = (30 * 30) / (2 * 9.8) ≈ 45.9 m

Solution for Time:

v = u + at
0 = 30 - 9.8t
t = 30 / 9.8 ≈ 3.06 s

These calculations assume no air resistance, which would be significant in real-world applications.

Problem 3: Falling from Rest

An object is released from rest and falls for 5 seconds. Find:

1. The distance it has fallen.
2. Its velocity just before hitting the ground.

Solution for Distance:

s = (1⁄2) * 9.8 * 5² = 122.5 m

Solution for Velocity:

v = 0 + 9.8 * 5 = 49 m/s

In summary, the study of free fall provides a fascinating insight into the fundamental laws of physics. Understanding free fall not only helps in visualizing motion but also lays the groundwork for more advanced studies in mechanics. Here are some key takeaways:

• All objects fall at the same rate in a vacuum, regardless of mass.
• The equations of motion provide tools to predict the path, speed, and time of objects in free fall.
• Free fall scenarios offer practical applications in numerous fields, from sports physics to engineering.

What causes an object to accelerate during free fall?

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Gravity is the sole force acting on an object in free fall, causing it to accelerate towards the center of the Earth at approximately 9.8 m/s².

Why do heavier objects not fall faster than lighter objects in a vacuum?

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In a vacuum, without air resistance, the force of gravity acts uniformly on all objects, meaning all masses experience the same acceleration due to gravity.

How does air resistance affect free fall?

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Air resistance opposes motion, effectively reducing acceleration for objects with larger surface areas or irregular shapes, thus altering the dynamics of free fall.