First slide

Geometric progression

Question

After striking the floor, a certain ball rebounds (4/5)th of height from which it has fallen. Then the total distance
that it travels before coming to rest, If it is gently dropped from a height of 120 m is

Moderate

A

1260 m
B

600m
C

1080 m
D

1008m

Solution

Initially the ball falls from a height of 120m. After striking the floor, it rebounds and goes to a height of $\frac{4}{5} \times (120) m$ Now, it falls from a height of $\frac{4}{5} \times (120)$ m and after rebounding goes to a height of $\frac{4}{5} (\frac{4}{5} (120))$ m. This process is continued till the ball comes to rest
Hence, the total distance travelled is
$120 + 120 (\frac{4}{5}) + 120 {(\frac{4}{5})}^{2} + . . . . . = \frac{120}{1 - \frac{4}{5}} = 600 m$

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