# QA – Placement Quizzes | Progressions | Question 10

A tennis ball is initially dropped from a height of 180 m. After striking the ground, it rebounds (3/5)th of the height from which it has fallen. The total distance that the ball travels before it comes to rest is:
(A) 540 m
(B) 600 m
(C) 720 m
(D) 900 m

Explanation: The total distance traveled by the ball is the sum of two infinite series:
a. Series 1: the distance traveled by the ball when it’s falling down
b. Series 2: the distance traveled by the ball when it’s bouncing up
S1 = a1 / (1 – r1) and S2 = a2 / (1 – r2)
S1 = 180 / (1 – 3/5) and S2 = (180 * 3/5) / (1 – 3/5)
S1 = 180 / (2/5) and S2 = 108 / (2/5)
S1 = 180 * 5/2 and S2 = 108 * 5/2
S1 = 450 and S2 = 270
Therefore, S = S1+S2 = 720 m.

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