The stories of a tall building are uniformly 10 feet in...

The stories of a tall building are uniformly 10 feet in height. A ball $A$ is dropped from the rooftop position shown. Determine the times required for it to pass the 10 feet of the first, tenth, and onehundredth stories (counted from the top). Neglect aerodynamic drag.

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Key Concepts

Free-Fall Motion

This concept refers to the motion of an object solely under the influence of gravity, with no other forces (like air resistance) acting on it. It simplifies the analysis since the only acceleration involved is due to gravity, allowing the use of standard kinematic equations.

Uniformly Accelerated Motion Equations

These equations describe the relationships between displacement, velocity, acceleration, and time for an object experiencing constant acceleration. An important equation is s = ut + (1/2)at², which is fundamental in solving problems involving objects in free-fall.

Gravitational Acceleration

This is the constant acceleration that objects experience when falling under Earth's gravity. In many cases, especially with imperial units, it is approximated as 32 ft/s². This parameter is essential for calculating the time and distance relationships in free-fall motion.

Reference Frames and Displacement

When analyzing problems involving heights or specific segments, such as building stories of a certain uniform height, identifying the correct reference point and understanding displacement relative to that point is crucial. This ensures that the calculated times correspond to the correct intervals along the fall path.

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