A ball is dropped from the top of a tower of height
MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A ball is dropped from the top of a tower of height 20m. On each bounce it rises to 53 times the height from which it fell.
(i) Show that the total vertical distance travelled by the ball (downward and upward together) after the first bounce can be expressed as the sum of an infinite geometric series.
(ii) Determine this total distance.
(iii) If the time taken for each downward or upward journey is proportional to the square root of the height of that journey, explain briefly whether the total time until the ball comes to rest is finite or infinite.