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What is the formula for speed as a function of time in free fall?
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V(T) = GT
How did Galileo’s thought experiment contribute to understanding gravity?
It demonstrated that attaching a heavier body to a lighter one would not change the rate at which they fall, leading to the conclusion that all bodies fall at the same rate to avoid logical contradictions.
What is the formula for distance fallen as a function of time?
S(T) = 1/2 GT^2
What experiment can illustrate the principle of all objects falling at the same rate in a vacuum?
A penny and feather falling experiment.
What is the foundational principle of the Law of Falling Bodies?
All bodies fall with the same constant acceleration in a vacuum.
What remains constant during free fall in a vacuum?
Acceleration (denoted as G for gravity).
Who invented calculus, and why is it significant in the study of motion and gravity?
Calculus was invented by Newton and Leibniz; it is essential for describing and analyzing motion, particularly for calculating instantaneous rates of change.
How is Galileo's law demonstrated at amusement parks like Magic Mountain?
The distances fallen in rides follow the odd number sequence, illustrating Galileo’s law of odd numbers.
Describe Galileo's Law of Odd Numbers.
It states that distances fallen by a body in equal intervals of time increase according to the odd numbers (1, 3, 5, ...).
What was Galileo's key insight about falling bodies?
All bodies fall at the same rate regardless of their weight.
What is the relationship between distance, speed, and acceleration in differential calculus?
Speed is the derivative of distance, and acceleration is the derivative of speed.
How does air resistance affect the fall of objects?
Air resistance causes objects to fall at different rates; removing air resistance (as in a vacuum) shows that all objects fall at the same rate.
What does the derivative measure in the context of motion?
The instantaneous rate of change.
Who were the key historical figures mentioned in the study of gravity?
Galileo, Isaac Newton, Albert Einstein
What is the relationship between distance fallen and time according to Galileo?
The distance fallen is proportional to the square of the time elapsed, expressed as S = CT^2.
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