MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A ball is dropped from a height of 10 meters. After each impact with the ground, it rebounds to 60% of the height from which it just fell. Assume no other forces are acting on the ball.
(a) Express, in terms of n, the total vertical distance Dn (sum of all upward and downward segments) that the ball has traveled up to and including its landing after the nth bounce.
(b) Derive a simplified formula for Dn that does not contain a summation symbol.
(c) Determine n→∞limDn or show that the limit does not exist. Clearly justify your conclusion.
(d) Interpret the value found in part (c) in the context of the physical motion of the ball.