A ball is dropped on a hard surface from a height of 7.2 meters. If on each rebound, it bounces 5/8 as high as

Question

its pevious bounce, how high does the ball bounce on the fifth bounce? What is the total distance traveled by the ball when it reaches the highest point of the fifth bounce? (I have an answer but I am just confused with the height of the first bounce. What is the distance after the first bounce? Should I multiply 7.2 by 5/8? But according to the problem the distance can be obtained by multiplying 5/8 to the previous bounce. Of course there is no previous bounce before the first bounce.)

Answer 1

By previous bounce, they mean the height it fell from. On any bounce, the ball will stop in the air and fall back down. It has the same effect as if you dropped the ball from that height. So yes, multiply 7.2 m by 5/8 to get 4.5 m after the first bounce, then again to get 2.8125 after the second; 1.7578125 after the third; 1.0986328125 after the fourth, and 0.6866455078125 after the fifth. Add these up to get about 18.06 m.

A simpler method would be to consider it a geometric series and use the sum and term formulas to compute, but for only five terms, this way is just as easy.

Hope this helps.

Answer 2

7.2 x 5/8 = 4.5 = first bounce
4.5 x 5/8 = 2.8125 = second bounce
2.8125 x 5/8 = 1.7578125 = thrird bounce
1.7578125 x 5/8 = 1.0986328125 = fourth bounce
1.0986328125 x 5/8 = 0.6866455078125 = fifth bouce

Total = 7.2 + (4.5 x 2) + (2.8125 x 2) + (1.7578125 x 2) + 1.0986328125 x 2) + 0.6866455078125

= 21.0245361328125

I hope thats right??!!

I would multiply 7.2 by 5/8 as if you didn't, the bounces would never get any smaller. I think the question should be reworded to say that it will bounce 5/8 of its previous maximum hieght or something similar. Bit confusing.

Answer 3

7.2 m = starting height
7.2 m · 5/8 = height on 1st bounce
7.2 m · 5/8 = height from peak of 1st bounce downward
2 · 7.2 m · 5²/8² = total distance in 2nd bounce
and so on...

Therefore, it bounces 7.2 m · 5^5/8^5 ≈ .095 m on the fifth bounce.

the total distance traveled until the peak of the 5th bounce is
7.2 m+ 2 · 7.2 m · 5/8 + 2 · 7.2 m · 5²/8² + 2 · 7.2 m · 5³/8³ + 2 · 7.2 m · 5^4/8^4 + 7.2 m · 5^5/8^5
≈ 21.02 m

^_^

Answer 4

The first bounce

7.2 x 5 = 36/8 = 4.5

Secound bounce

4.5 x 5 = 22.5/8 = 2.8125

Third bounce

2.8125 x 5 = 14.0625/8 = 1.7578125

Fourth bounce

1.7578125 x 5 = 8.7890625/8 = 1.098632813

Fifth bounce

1.098632813 x 5 =5.493164063/8 = 0.686645508

Answer 5

you can consider the first drop as the zeroth bounce. Therefore the first bounce will be 7.2 X 5/8, second bounce will be 7.2 X 5/8 X 5/8.

Answer 6

If on each rebound, it bounces 5/8 as high as
its pevious bounce then we can say that
1st bounce=7.2 meter*5/8=4.5 meter
2 nd bounce=4.5*5/8=2.8125 meter
3 rd bounce=2.8125*5/8=1.7578125 meter
4 th bounce=1.7578125 *5/8=1.0986328125 meter
5 th bounce=1.0986328125 *5/8=.6866455 meter.
So, total distance travelled on all bounces=10.85559 meter
total distance travelled on all bounces and returns=10.85559*2 meter
=21.71 meter
if we have to consider total distance travelled including 1 st fall from 7.2 meter height , then total distance travelled=21.71+7.2=28.91 meter

Answer 7

u shud assume that previous bounce befor 1st is initial height. so the height of N-th bounce wii be 7.2*(5/8)^N

and ur answer wil be 7.2*(5/8)^5

Answer 8

0.6866455Mts