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5. A rubber ball dropped on a hard surface takes a sequence of bounces, each one 3/5 as high as the preceding one. If this ball is dropped from a height of 15 feet, what is the total distance it has traveled after it hits the surface the fifth time?


The answer is 54 and 21/125 ft, but why?

A rubber ball dropped on a hard surface takes a sequence of bounces, each one 3/5 as high as the preceding one. If this ball is dropped from a height of 15 feet, what is the total distance it has traveled after it hits the surface the fifth time?

Dwn.Up.Dwn.Up.Dwn..Up...Dwn...Up...Dwn
15..9...9.5.4.5.4.3.24.3.24.1.944.1.944

Ssumming yields 54.168 = 54 21/125 feet.

  • math -

    Guys, here is the answer.

    Ball is dropped from a height of 15 feet and each bounce it goes to 3/5 as high as the preceding one.

    Now, total distance traveled in:
    1st drop:15 (till it hits the ground)
    2nd drop:(15*3/5)=9*2=18 [Multiply by 2 as distance to go up (15*3/5) and to come down (15*3/5),so multiply by 2]
    3rd drop: (9*3/5)=5.4*2 =10.8
    4th drop: (5.4*3/5)=3.24*2 =6.48
    5th drop: (3.24*3/5)=1.94*2= 3.888 (now ball will hit the ground after 5th fall)

    total distance: distance in 1st drop+ 2nd drop+3rd drop+4th drop+5th drop.
    = 15+18+10.8+6.48+3.888=54.168

    Hope this helps....

  • math -

    It's a sort og geometric series with limiting sum. Please I need a perfect formula to calculate it instead of the normal addition

  • math -

    each time a bouncy ball bounce, it bounces to half the height from which it had just fallen. if jack drops a ball from a building and it rises to a height of 24 metres, how high will it bounce on the fifth bounce?

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