Mathematics

Problem

A ball is dropped from a height of

125\,\text{m}

and rebounds to

60\%

of the height from which it falls after each bounce. a. (i) Express the height reached after the

n

th bounce in the form of a sequence and state the common ratio. b. (ii) Calculate the height reached after the

6

th bounce. c. (iii) Determine the smallest integer

n

for which the height after the

n

th bounce is less than

5\,\text{m}

. Show all working steps.