Question

That Is the Way the Ball Bounces!

Sam completed the following procedure in his Algebra II class:

Choose a height from which all of the balls will be dropped one at a time.
Vertically along the blank wall, set up the measuring tape and step stool or chair.
Have a family member or friend stand on a step stool and drop one of the balls from the chosen height. Drop the ball close enough to the measuring tape to be able to record height, but not touch the tape.
Face the measuring tape, opposite the ball's starting point from about 7 or 8 feet high.

Answer 1

As the ball falls, measure the height the ball reaches after each bounce for four consecutive bounces. (You may need to repeat the process to ensure that your measurements are accurate. You may choose to video each drop to assure accuracy.)
illustration showing a ball bouncing 4 times if someone dropped the ball from 7 or 8 feet high

He recorded the height of each bounce, beginning with the height from which the ball originally fell, in the chart below:
Ball 1 Description Ball 2 Description Ball 3 Description
Height 1
(starting point)
3 ft
3 ft
3 ft
Height 2
2.4
1.9
0.9
Height 3
1.9
1.2
0.3
Height 4
1.5
0.8
0.1
Height 5
1.2
0.5
0.02

Answer 2

Using complete sentences, answer the following questions:
What is the average common ratio between the successive height values of ball 1? Ball 2? Ball 3? Experimental errors may cause common ratios to have some variances within the data for one ball. Use the average common ratio.

What is the height of each ball on the fifth bounce (i.e., Height 6)? Use the geometric sequence formula, an = a1rn – 1 and show your work.

What is the total distance of the height each ball has traveled in the first five heights? Use the geometric series formula, Sn = the quantity of a sub 1 minus a sub 1 times r to the n power, all over 1 minus r and show your work.

Answer 3

Please Help Me !

Answer 4

@iGreen @hartnn @AnswerMyQuestions

Answer 5

could you start ? where are you stuck?

Answer 6

Ok... Um what im not uderstanding is do we create our own data or we use the data given ?

Answer 7

the data given,
for ball 1
the heights are 3,2.4,1.9,1.5,1.2

find the average common ratio

Answer 8

like find the ratio of next height to current height, for all heights and take the average

Answer 9

1.25

Answer 10

its not 3/2.4

it'll be 2.4/3 =....
1.9/2.4 =....
1.5/1.9....
and so on,
and then take the average of all the above answers

Answer 11

ok so i've got
0.8 , 0.78 , 0.79 , 0.8

Answer 12

oops 0.79 , 0.78

Answer 13

so what is the average of all those ?

Answer 14

0.63

Answer 15

can't be ... did you do any calculation mistake?

Answer 16

Hmm let me see i added it up and divided by the number of heights

Answer 17

3.17 / 5

Answer 18

divide it by number of ratios = 4 :)

Answer 19

oops sorry

Answer 20

0.79

Answer 21

thats you common ratio = r for 1st ball
do it for ball2 and ball 3 too :)

Answer 22

Ok give me a sec

Answer 23

Ball 2 is 0.63

Answer 24

you want me to verify your answers or are you confident of your workings?

Answer 25

I would like you to verify im not usually very good at these things

Answer 26

For ball 3 its 1.16

Answer 27

go to the next part
\(a_n = a_1 r^{n-1}\)

a_1 is the first height.
r = we just calculated
n= 6 (we need 6th height)

Answer 28

for each balls, you'll get different answers because a_1 and r are different

Answer 29

Ok im going to try

Answer 30

Like this right ?
an = (3)0.79 ^ 6 -1

Answer 31

yes, be careful with the brackets


(3)[0.79 ^ (6 -1)]

(3)*[0.79 ^ 5]

Answer 32

Ohhh Ok thats better

Answer 33

0.92

Answer 34

0.29 and 6.30

Answer 35

Am i correct ?

Answer 36

i got 0.954 for first, but 0.92 is close enough

Answer 37

0.304 for second, and 0.29 is close enough too :)

Answer 38

for ball 3, r is not 1.16 ...
try again?

Answer 39

ok

Answer 40

ok i got it now its 0.29

Answer 41

yeah, thats correct
so
3*[0.29^5]

Answer 42

0.00

Answer 43

lol
can't be 0....
its 0.006

Answer 44

Oh ok :)

Answer 45

Sn = 3 - 3 (0.79) 5 / 1 - 0.79 =
Sn = 3 - 3 (0.63)5 / 1 - 0.63 =
Sn = 3- 3 (0.006)5 / 1 - 0.006

Answer 46

Now like ^ that right ?

Answer 47

yes, those are correct

Sn = [3 - 3 (0.79) 5 ]/ [1 - 0.79] =

Answer 48

Is it 0.2

Answer 49

[3 - 3 (0.79) 5 ]/ [1 - 0.79]
i get 9.889

Answer 50

How did you do it ?

Answer 51

calculator

Answer 52

http://www.wolframalpha.com/input/?i=%5B3+-+3+%280.79%29%5E5+%5D%2F+%5B1+-+0.79%5D

Answer 53

Mine wont do it ! It gave me 17.42 for the second one

Answer 54

Wait 7.30 for the second one

Answer 55

And 3.01 for last one

Answer 56

http://www.wolframalpha.com/input/?i=%5B3+-+3+%280.63%29%5E5%5D+%2F+%5B1+-+0.63%5D

is correct :)

Answer 57

THANKKKKK U SO MUCHHHHH!!!! Ur A Life Saver.... Mind Helping Me With One More Question

Answer 58

Robbie the Robot is on a weather satellite orbiting Earth about 3600 km above the surface. The Earth’s radius is about 6400 km. He has had a malfunction in his output device, and the satellite is traveling without communication. His last report was only in terms of trigonometric values and was only partially received. It said, sin Θ < 0….. and then he was lost again.
Part 1: Create a set of coordinates that would be reasonable for Robbie’s position in space and satisfy his last, partial report. Using complete sentences, describe Robbie’s location and your reasoning.

Answer 59

sorry, wish i had that much more time...

Answer 60

Oh no worrys you have done enough... Thank you so much !!