A ball is dropped from a height of 20 m onto a perfectly horizontal floor
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A ball is dropped from a height of 20 m onto a perfectly horizontal floor. After each impact with the floor it rises to 70 % of the height from which it had just fallen.
(i) Obtain an expression for the height to which the ball rises after the nth rebound.
(ii) Show that the total vertical distance travelled by the ball up to and including the nth rebound can be written in the form Dn=20+2kn, where kn is to be determined.
(iii) Hence calculate the total vertical distance the ball travels before coming to rest.
(iv) After how many complete rebounds will the ball first rise to a height less than 1 m? (Give your answer correct to the nearest integer.)