Question

Assume that the ball rebounds the same percentage on each bounce. using the initial drop height and the height after the first bounce, find the common ratio, r. note: round r to three decimal places. use this formula: (3 points: 2 points for showing your work, 1 point for the answer)

Answer 1

Let from the height at which ball was thrown = h units

It is given that , ball rebounds the same percentage on each bounce.

Let it rebounds by k % after each bounce.

Height that ball attains after thrown from height h(on 1 st bounce)=
`h + (h k)/(100)=h * (1+(k)/(100))`

Height that ball attains after thrown from height h (on 2 n d bounce)=
`h * (1+(k)/(100))+h * (1+(k)/(100))* (k)/(100)=h * (1+(k)/(100))^2`

Similarly, the pattern will form geometric sequence.

S=
`h +h * (1+(k)/(100))+h * (1+(k)/(100))^2+h * (1+(k)/(100))^3+.........`

So, Common Ratio =
`\frac{\text{2nd term}}{\text{1 st term}}=1 +(k)/(100)`

Common Ratio= 1 + the percentage by which ball rebounds after each bounce

the percentage by which ball rebounds after each bounce= negative integer= k is negative integer.