Question

A ball is dropped from a height of 128 m. It bounces back rising to
a height of 64 m. Each time it further touches the floor, it rises to the
height of half the height it fell from before the previous bounce. Find
the total distance travelled by the ball.​

Answer 1

The total distance traveled by the ball is 384 m.

Solution

• As we know that Initial fall is s1 = 128 m
• Now, next rise and fall s2 = 2 ⋅ 1 / 2 ⋅ 128m
• For the third rise and fall s3 = 2 ⋅ (1 / 2^2)128 m
• For fourth rise and fall s4 = 2 ⋅ (1 / 2^3) 128 m
• Now the total path covered by the ball is
• S = i=∞

              ∑

             I = 1si

• = 128 + 128 (1 + 1 / 2 + 1 / 2^2+.....up to infinity ∞)
• = 128 + 128 (1 ÷ 1 − 1/2)
• = 128 + 128 (1 / 1 ÷ 2)
• = 3 ⋅ 128 = 384 m

Thus the total distance traveled by the ball is 384 m.

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