Question

On each bounce, a ball dropped from 100 feet rises to

1/2
the height from which it has fallen. How high does the
ball rise, in feet, on the 10th bounce?

Answer 1

Answer: 0.09766 feet (0.10 rounded to the nearest tenth)

Explanation:

Answer 2

0.5 feet or 6 inches

Explanation:

To find the height of the ball on the 10th bounce, we need to use the given equations. Let h be the height of the ball in feet after n bounces (including the initial drop), and k be a constant that depends on the coefficient of restitution. We also have a starting height of 10 feet and a height of 2 feet after 5 bounces, so:

10 = k * 5h

4 = k * 10h

We can solve these two equations for k, then use them to solve for h:

k = (10 - 4) / (5 * 4) = 0.5

Substituting this value into the original height equation, we get:

h = k^2 * 2 = 0.25 * 2 = 0.5

So, the height of the ball on the 10th bounce is 0.5 feet, or 6 inches.