Question

When a ball is dropped, the height it reaches after it bounces is a fraction of its original drop height. What fraction of its original height does each ball bounce up to after the third bounce? basketball: (3/4)exp x tennis ball: (2/3)exp x softball: (3/10)exp x

Answer 1

The ball's height after each bounce is a fraction of its original drop height. After the third bounce, a basketball reaches (3/4)exp3 of its original drop height, a tennis ball reaches (2/3)exp3, and a softball reaches (3/10)exp3.

Step-by-step explanation:

The height a ball reaches after being bounced is often described by a multiplicative factor of its original height, indicating energy loss due to various factors like friction. This is usually represented as an exponential factor for each bounce. For instance, in your case:

• a basketball will reach a height equivalent to (3/4)exp3 of its original drop height after the third bounce, assuming that the basketball retains 3/4 of its drop height upon each bounce.
• a tennis ball will reach a height equivalent to (2/3)exp3 of its original drop height after the third bounce, assuming that the tennis ball retains 2/3 of its drop height upon each bounce.
• a softball will reach a height equivalent to (3/10)exp3 of its original drop height after the third bounce, assuming that the softball retains 3/10 of its drop height upon each bounce.

Learn more about Bounce Height