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

Step-by-step 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((14)/(15))^n<1`

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

`(10\left((14)/(15)\right)^n)/(10)<(1)/(10)`
`\left((14)/(15)\right)^n<(1)/(10)`

Applying exponents rule

`\begin{gathered} n>\log _{(14)/(15)}\left((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=(a)/(1-r)=(10)/(1-(14)/(15))=(10)/((1)/(15))=10*15=150`

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