A ball is dropped from a height meters onto a perfectly vertical surface
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A ball is dropped from a height H meters onto a perfectly vertical surface. After each impact it rebounds to a fraction p (with 0<p<1) of the height from which it just fell. Assume the process continues indefinitely and that air resistance is negligible.
(a) Express the total vertical distance traveled by the ball, from the instant of release to the end of all rebounds, as an infinite series in terms of H and p. Clearly justify the structure of your series.
(b) Determine the set of all real values of p for which the total vertical distance you obtained in part (a) is finite. Provide a complete explanation.
(c) For H=2 meters and p=0.6, calculate the exact total vertical distance traveled by the ball. Present your work in a logically ordered sequence of steps.