Question

A Super Happy Fun Ball is dropped from a height of 10 feet and rebounds 1415 of the distance from which it fell.How many times will it bounce before its rebound is less than 1 foot?It will bounce times before its rebound is less than 1 foot.How far will the ball travel before it comes to rest on the ground?It will travel feet before it comes to rest on the ground.

Answer 1

Explanation

Part A

To solve the question, we will set up the equation to get the number of times it rebounds is less than 1 foot

$H=10(\frac{14}{15})^n<1$

To solve for n, we will have to divide both sides by 10

$\frac{10\left(\frac{14}{15}\right)^n}{10}<\frac{1}{10}$$\left(\frac{14}{15}\right)^n<\frac{1}{10}$

Applying exponents rule

$\begin{gathered} n>\log _{\frac{14}{15}}\left(\frac{1}{10}\right) \\ \\ n>33.3742 \end{gathered}$

Therefore, the ball must bounce more than 33 times to attain a height of less than 1 foot

Thus, it has to bounce 34 times or more

Part 2

To get the how far it will travel before it comes to rest

We will have to get the sum of the heights as it tends to infinity

$S=\frac{a}{1-r}=\frac{10}{1-\frac{14}{15}}=\frac{10}{\frac{1}{15}}=10\times15=150$

Thus, the ball will have to travel a distance of 150 feet before it comes to rest