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$$\text{A ''super ball'' is dropped from a window 16 meters above the ground. On each bounce it rises \frac34 the distance of the preceding high point. The ball is caught when it reached the high point after hitting the ground for the third time. To the nearest meter, how far has it travelled?}$$

Jul 18, 2019

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When it falls the first time, it goes 16 meters.

When it goes up the first time, it goes up 16*3/4 = 12 meters.

When it falls the second time, it goes 12 meters.

When if goes up the second time, it goes up 12*3/4 meters = 9 meters.

When it falls the third time, it goes 9 meters.

When it goes up the third time, it goes 9*3/4 = 27/4 meters.

16+12+12+9+9+27/4 = 16+24+18+27/4 = (64+96+72+27)/4 = (160+99)/4 = 259/4.

You are very welcome!

:P

Jul 18, 2019