Coefficient of restitution from bounce heights: A ball is dropped from 2.25 m onto a smooth floor and rises to 1.00 m after the bounce. Assuming vertical impact and negligible air resistance, compute the coefficient of restitution between the ball and the floor.

Introduction / Context:The coefficient of restitution e relates rebound speed to impact speed along the line of impact. For vertical drops, energy relations yield a simple formula in terms of drop and rebound heights, which is widely used in sports engineering and material testing.

Given Data / Assumptions:

• Drop height h1 = 2.25 m.
• Rebound height h2 = 1.00 m.
• Neglect air resistance; vertical motion only.

Concept / Approach:For vertical impacts without air drag, e = (rebound speed) / (impact speed). Using v = √(2 g h), we get e = √(h2 / h1).

Step-by-Step Solution:

Verification / Alternative check:If h2 = h1 (perfectly elastic), e = 1. If h2 = 0 (perfectly plastic), e = 0. Our result lies between 0 and 1, as expected.

Why Other Options Are Wrong:

• 0.33, 0.44, 0.57, 0.77: do not satisfy e = √(1/2.25).

Common Pitfalls:Taking a linear ratio rather than square root; mixing heights with velocities directly.

Final Answer:0.67