Q:

# 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)

Accepted Solution

A:
Let from the height at which ball was thrown = h unitsIt 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)= $$h + \frac{h k}{100}=h \times (1+\frac{k}{100})$$Height that ball attains after thrown from height h (on 2 n d bounce)= $$h \times (1+\frac{k}{100})+h \times (1+\frac{k}{100})\times \frac{k}{100}=h \times (1+\frac{k}{100})^2$$Similarly, the pattern will form geometric sequence.S= $$h +h \times (1+\frac{k}{100})+h \times (1+\frac{k}{100})^2+h \times (1+\frac{k}{100})^3+.........$$So, Common Ratio = $$\frac{\text{2nd term}}{\text{1 st term}}=1 +\frac{k}{100}$$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.