"Bouncing Efficiency: Which Ball Reaches New Heights?"

To determine which ball bounces with the most efficiency, you can calculate the coefficient of restitution, which is the ratio of the height the ball bounces back to the height it was dropped from. This is essentially a measure of the ball's efficiency in retaining energy during the bounce. The formula for the coefficient of restitution (efficiency) is: \[ \text{Efficiency} = \frac{\text{bounce height}}{\text{drop height}} \] Let's calculate this for each ball: 1. For option a: \[ \text{Efficiency} = \frac{6m}{10m} = 0.6 \] 2. For option b: \[ \text{Efficiency} = \frac{10m}{12m} \approx 0.833 \] 3. For option c: \[ \text{Efficiency} = \frac{6m}{12m} = 0.5 \] 4. For option d: \[ \text{Efficiency} = \frac{2m}{10m} = 0.2 \] Comparing these values: - Option a: 0.6 - Option b: 0.833 (approximately) - Option c: 0.5 - Option d: 0.2 Thus, the ball in option b, which is dropped from 12m and bounces to a new height of 10m, has the highest efficiency at approximately 0.833. Therefore, option b is the most efficient.