To test the quality of a tennis ball, you drop it onto the...

To test the quality of a tennis ball, you drop it onto the floor from a height of $4.00 \mathrm{~m}$. It rebounds to a height of $2.00 \mathrm{~m}$. If the ball is in contact with the floor for $12.0 \mathrm{~ms}$, (a) what is the magnitude of its average acccleration during that contact and (b) is the average acceleration up or down?

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Key Concepts

Sign Conventions in Motion

In problems involving vector quantities like velocity and acceleration, choosing a consistent sign convention (e.g., assigning positive for upward and negative for downward motion) is essential. This ensures that the computed changes in velocity and acceleration correctly reflect the directionality of the movement, which is crucial for interpreting the results accurately.

Kinematic Equations

Kinematic equations relate an object's displacement, initial velocity, final velocity, acceleration, and time under constant acceleration conditions. They are used to determine the velocities before and after collision points, such as the speed just before the ball hits the ground and the speed after it rebounds.

Average Acceleration

Average acceleration is defined as the change in velocity divided by the time interval over which the change occurs. It is a vector that indicates both the magnitude of the acceleration and its direction, and is critical in analyzing motion during intervals of short duration, such as a collision or rebound.

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