Question

Child 1 throws a snowball horizontally from a rooftop; child 2 throws a snowball straight down from the same rooftop. Once in flight, is the acceleration of snowball 2 greater than, less than, or equal to the acceleration of snowball 1 ?

Short answer

The acceleration of both snowballs is equal due to gravity.

Step-by-step solution

Identify Forces Involved

Both snowballs are subject only to the force of gravity once they are in flight. This means the only acceleration that affects them is gravitational acceleration.

Understand the Gravitational Acceleration

The gravitational acceleration on Earth is approximately constant and equal to 9.81 m/s². It affects all objects the same way regardless of their initial velocity or the direction of their motion.

Acceleration of Each Snowball

Since gravity acts on both snowballs equally and is the only force acting on them once in flight, both snowballs have the same acceleration of 9.81 m/s² downward, due to gravity.

Conclusion on Acceleration

As both snowballs experience the same gravitational acceleration, the acceleration of snowball 2 (thrown straight down) is equal to the acceleration of snowball 1 (thrown horizontally).

Key concepts

Gravitational Acceleration

In the world of physics, gravitational acceleration is a key concept that helps us understand how objects move under the force of gravity. On Earth, this constant is approximately 9.81 m/s². This means that regardless of how an object is projected, whether straight down, horizontally, or at an angle, gravity will pull it downward at the same rate.
This force acts uniformly on all objects, which is why when considering a flat plane with no air resistance, two falling objects dropped simultaneously will hit the ground at the same time, even if they have different weights. It is important to note that gravitational acceleration affects the vertical motion, not the horizontal motion. This idea simplifies projectile motion problems, as one can calculate vertical and horizontal movements separately.

Newton's Laws of Motion

Sir Isaac Newton gifted us with three laws of motion that form the foundation of classical mechanics. Newton's first law, the law of inertia, tells us that an object will remain at rest or move at a constant velocity unless acted on by an external force. His second law defines the relation between force, mass, and acceleration, expressed by the equation: \[ F = ma \] where \( F \) is force, \( m \) is mass, and \( a \) is acceleration.
His third law states that for every action, there is an equal and opposite reaction.

• These laws help us understand why, in our exercise, both snowballs subjected to the same gravitational force experience the same acceleration.
• Since the only force acting on the snowballs once they're in flight is gravity, it confirms that both snowballs have the same acceleration, not affected by their direction of throw.

Horizontal and Vertical Motion

When we talk about projectile motion, it involves understanding both horizontal and vertical components of movement separately.
In our exercise example, child 1's snowball thrown horizontally initially moves due to the force applied by the throw. Meanwhile, child 2's snowball initially moves downward purely due to gravity.

• The horizontal motion of the snowball is not affected by gravity until it eventually hits the ground. This means the snowball will travel with a constant horizontal velocity (ignoring air resistance).
• The vertical motion, however, is influenced by gravitational acceleration, causing the snowball to accelerate downwards at 9.81 m/s².

In essence, whether thrown straight or horizontally, the vertical motion of the snowball is constituted equally by gravity, leading us to recognize why both snowballs accelerate downward at the same rate.