MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A ball is dropped from a height of 10 m. After each impact with the ground it rises to 80 % of the height from which it fell.
(i) Write down the first four rebound heights after the initial drop.
(ii) Show that the total vertical distance covered by the ball after n rebounds is given by an expression of the form Dn=10+2×(sum of a finite geometric progression).
(iii) Calculate the total distance travelled up to and including the fifth rebound.
(iv) Find, correct to two decimal places, the distance the ball will have travelled in total if it continues to bounce indefinitely.