Discussion
A ball is dropped from a height of 120 meters. It rebounds two-thirds of the height from which it falls. What is the total distance it travels before coming to rest?
Answer: C
This is a trick question. The answer should be 600 m. Let's re-calculate. Initial drop distance = 120m. After that, it rebounds and falls. Rebound 1: up \(120 \times 2/3 = 80\), down 80. Rebound 2: up \(80 \times 2/3 = 160/3\), down 160/3. The total distance is \(120 + 2 \times (80 + 160/3 + ...)\). The series in the bracket is a G.P. with \(a=80, r=2/3\). Its sum is \(\frac{a}{1-r} = \frac{80}{1-2/3} = \frac{80}{1/3} = 240\). Total distance = \(120 + 2 \times 240 = 120 + 480 = 600\) m.
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