Question

A rubber ball is dropped onto a hard surface from a height of 9 feet, and it bounces up and down. At each bounce it rises to 80% of the height from which it fell.
a. Find a formula for h(n), the height in inches reached by the ball on bounce n.
h(n) =

b. How high will the ball bounce on the 10 bounce?


c. How many bounces before the ball rises no higher than an inch?

Answer 1

There are 12 inches in a foot, so 9ft = 108in. Also, 80% = 0.8. Therefore the formula is: h(n) = 108 * 0.8^n. To find the bounce height after 10 bounces, substitute n=10 into the equation: h(n) = 108 * 0.8^10 = 11.60in (2.d.p.). Finally to find how many bounces happen before the height is less than one inch, substitute h(n) = 1, then rearrage with logarithms to solve for the power, x: 108 * 0.8^x = 1; 0.8^x = 1/108; Ln(0.8^x) = ln(1/108); xln(0.8) = ln(1\108); x = ln(1/108) / ln(0.8) = -4.682 / -0.223 = 21 bounces