Instructions

Program in C$++$

Suppose that we drop a ball on the ground and see how high it bounces. As you know from experience, it never bounces to the s height from which you drop it$.$ Instead, its height is reduced. We can model that reduction with what we could call a "coefficient rebound."

If a ball dropped from a height of $10$ meters bounces $8$ m high, then we say that the coefficient of rebound is $0\mathrm{.}8,$ and the total distance traveled by the ball is $18$ m after one bounce. After a second bounce, the ball will have traveled $\backslash (10\backslash$mathrm$\{$~m$\}+8\backslash$mathrm$\{$~m$\}+8\backslash$mathrm$\{$~m$\}+6\mathrm{.}4\backslash$mathrm$\{$~m$\}\backslash ).$ you can see, the distance traveled for each bounce is the distance down to the floor, plus $0\mathrm{.}8$ of that as the ball comes back up:

$\backslash [$

$\backslash$begin$\{$array$\}\{$c$\}$

$10\backslash$mathrm$\{$~m$\}(\backslash$text $\{$ down $\})+8\backslash$mathrm$\{$~m$\}(\backslash$mathrm$\{$up$\})+8\backslash$mathrm$\{$~m$\}(\backslash$text $\{$ down $\})+6\mathrm{.}4\backslash$mathrm$\{$~m$\}\backslash$text $\{($up$)\}\backslash \backslash$

$\backslash$text $\{$ bounce $\}1+\backslash$text $\{$ bounce $\}2$

$\backslash$end$\{$array$\}$

$\backslash ]$

$1.$ Write a program that will calculate the total distance traveled by the ball over a number of bounces input by the user. Assu that it is dropped from $10$ meters and that the coefficient of rebound is $0\mathrm{.}8.$ Is a for loop or a while loop more appropriat for this problem, and why? $($Write your answer as comments in the code.$)$

$2.$ Write a similar program that will tell how many bounces it took for the ball to travel a distance specified by the user. For instance, if the user inputs $20($for $20$ meters$),$ the program will report $2$ bounces. $($The first bounce covers $18$ m $,$ so $20$ m requires part of a second bounce too.$)$ Is a for loop or a while loop more appropriate for this problem, and why?