SOLUTION: A ball rebounds 7/8 as high as it bounced on the previous bounce and is dropped from a height of eight feet. How high does it bounce on the fourth bounce and how far has it travele
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Question 484916: A ball rebounds 7/8 as high as it bounced on the previous bounce and is dropped from a height of eight feet. How high does it bounce on the fourth bounce and how far has it traveled after the fourth bounce?
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You can put this solution on YOUR website! A ball rebounds 7/8 as high as it bounced on the previous bounce and is dropped from a height of eight feet. How high does it bounce on the fourth bounce
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ht = 8*(7/8)^4 = 8*2401/4096 = 2401/415 ft
=~ 4.689 ft on the 4th bounce
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and how far has it traveled after the fourth bounce?
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d = 8 + 8*(7/8)*2 + 8*(7/8)^2*2 + 8*(7/8)^3*2 + 8*(7/8)^4 to its apogee the 4th time.
d = 8 + 16*(7/8 + 49/64 + 343/512) + 8*2401/4096 to the apogee the 4th time.
d = 8 + 14 + 49/4 + 343/32 + 2401/512
d = 22 + (6272 + 5488 + 2401)/512
d = 22 + 14161/512
d = 49 + 337/512 feet
d =~ 49.582 feet at its highest point after the 4th bounce
