A ball is dropped from the roof of a building. It hits the...

A ball is dropped from the roof of a building. It hits the ground and it is caught at its original height 5.0 s later. a) What was the speed of the ball just before it hits the ground? b) How tall was the building? c) You are watching from a window $2.5 \mathrm{~m}$ above the ground. The window opening is $1.2 \mathrm{~m}$ from the top to the bottom. At what time after the ball was dropped did you first see the ball in the window?

A ball is dropped from the roof of a building. It hits the ground and it is caught at its original height 5.0 s later.
a) What was the speed of the ball just before it hits the ground?
b) How tall was the building?
c) You are watching from a window $2.5 \mathrm{~m}$ above the ground. The window opening is $1.2 \mathrm{~m}$ from the top to the bottom. At what time after the ball was dropped did you first see the ball in the window?

Key Concepts

Uniformly Accelerated Motion

Uniformly accelerated motion refers to movement where the acceleration is constant throughout the motion. This concept is fundamental in analyzing objects in free-fall, where the gravitational acceleration (g) remains nearly constant, allowing the use of standard kinematic equations.

Kinematic Equations

Kinematic equations are the mathematical relationships between displacement, velocity, acceleration, and time used to describe motion. These equations provide a robust mathematical framework to solve problems involving objects moving under constant acceleration, such as those in free-fall.

Free Fall

Free fall is a type of motion experienced by objects when only gravity acts upon them, with negligible influences from air resistance. In free-fall, an object will accelerate at a constant rate (approximately 9.8 m/s² near the Earth's surface), which simplifies the calculation of velocities and displacements using kinematic formulas.

Time of Flight and Motion Symmetry

The time of flight represents the total duration that an object is in motion, and in cases where an object is dropped and later returns to the same height, the motion is symmetric. This symmetry implies that the time taken to descend is equal to the time taken to ascend, which is a key insight used to solve for parameters like building height and velocity at impact.

Determining Displacement at Specific Times

This concept involves calculating an object's position at particular moments using the kinematic equations. By setting the displacement equal to specific values, one can determine the exact times at which the object reaches predetermined heights or passes particular points in its trajectory.

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