A soft tennis ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height

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A soft tennis ball is dropped onto a hard floor from a...

A soft tennis ball is dropped onto a hard floor from a height of $1.50 \mathrm{m}$ and rebounds to a height of $1.10 \mathrm{m}$. (a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after it leaves the floor on its way back up. (c) Calculate its acceleration during contact with the floor if that contact lasts $3.50 \mathrm{ms}\left(3.50 \times 10^{-3} \mathrm{s}\right)(\mathrm{d})$ How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid?

A soft tennis ball is dropped onto a hard floor from a height of $1.50 \mathrm{m}$ and rebounds to a height of $1.10 \mathrm{m}$.
(a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after it leaves the floor on its way back up. (c) Calculate its acceleration during contact with the floor if that contact lasts $3.50 \mathrm{ms}\left(3.50 \times 10^{-3} \mathrm{s}\right)(\mathrm{d})$
How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid?

Key Concepts

Gravitational Acceleration

This concept refers to the constant acceleration imparted by Earth’s gravity on any object in free fall, typically taken as approximately 9.8 m/s². It plays a key role in predicting how an object’s velocity and position change over time when it is moving under the influence of gravity alone, without air resistance or other forces.

Kinematic Equations for Constant Acceleration

These equations describe the motion of objects under constant acceleration and relate displacement, initial and final velocities, acceleration, and time. They are fundamental for solving problems involving objects in free-fall or any uniformly accelerated motion, allowing one to compute unknown parameters when given sufficient information.

Average Acceleration

Average acceleration is defined as the change in velocity divided by the time interval over which the change occurs. This concept is essential in analyzing situations with rapid changes in an object’s speed or direction, such as during collisions or bounces, where the acceleration may be very high for a brief period.

Collision Dynamics and Deformation

When an object collides with a surface and rebounds, understanding the dynamics of the collision involves analyzing the forces during the very short contact time. This concept includes calculating acceleration during impact and estimating the deformation (or compression) of the object, even when the surface is considered completely rigid. It integrates both kinematic principles and material behavior under high-speed impacts.

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