Question

A ball is dropped from a height of 1 metre. If it reaches 0.7 times the height of the previous bounce at each bounce, work out how many times the ball bounces until the height is less than 1 centimetre.

Answer 1

Could you show us what you've done so far please?

Answer 2

I haven't done the question yet. I think I know how to do it but I think there might be a faster way @Azteck

Answer 3

Okay. So every bounce of the ball it reaches 0.7 times the height of it's previous height.
Let's form a sequence. ;)
\[\large 1+0.7+0.7(0.7)+0.7^3+....\]

Answer 4

Now we use the geometric formula for a term.

Answer 5

Is this your way of doing it or were you thinking of something else?

Answer 6

So the number of terms "n" is what you're looking for because "n" in this question would be the number of bounces the ball generates.

Answer 7

Do you know what the formula of finding a term in a geometric sequence is?

Answer 8

You can form a geometric series, but it doesn't really matter in this question. @Sepeario Are you there?

Answer 9

\[h(t)=1\ m*0.7^t\]
t is number of times bounced

so for example, after one bounce t = 1, \[h(1)=1\ m*0.7^{(1)}=0.7\ m\]

Answer 10

Solve h(t) ≤ 1 cm aka h(t) ≤ 0.01 m

Answer 11

\[0.7^t ≤ 0.01\]\[ln0.7^t≤ln0.01\]\[t\ ln0.7≤ln0.01\]\[t≤ln0.01/ln0.7\]

Answer 12

t ≤ http://www.wolframalpha.com/input/?i=ln0.01%2Fln0.7&dataset=

t ≤ 12.9 bounces

Answer 13

whole bounces, it would take 13 bounces. \[1\ m*0.7^{(13)}=0.0096\ m≤0.01\ m\]

Answer 14

@Azteck I don't know what the formula of finding a term in a geometric sequence is.

Answer 15

http://openstudy.com/study#/updates/51789029e4b0515c2da15359

Answer 16

\[\large T_{n}=ar^{n-1}\]
where:
T_n stands for the nth term.
"a" is the first term of the sequence
"r" is the common ratio in the sequence
"n" is the number of terms in the sequence.
What you're trying to find is "n".

Answer 17

@Azteck Whats wrong with what I did

Answer 18

Because you know what the first term is, the common ratio and the n-th term which is 1cm.

Answer 19

And nothing's wrong with what you did except you just did it in a different way. The only problem is that you didn't guide Sepeario through what you did, step by step. You just gave out, what is commonly referred to in some tutorial centres, the worked out solution.

Answer 20

centers*

Answer 21

lol

Answer 22

@Sepeario Are you confused about what I posted above about the formula for the geometric sequence or have you not learnt series and sequences?

Answer 23

I haven't learnt this kind of stuff b4, thanks for teaching me. It's definitely new to me. @Azteck

Answer 24

I see your next question you posted involves series and sequences, so you have done a bit but maybe haven't paid fulla ttention in class or something.

Answer 25

full attention*

Answer 26

Oh, so you haven't learnt series and sequences but you're doing questions involving it anyway?

Answer 27

So @Sepeario, could you use that formula and substitute your values from your question. ANd then you can show me your equation with the variable n that you're meant to find.

Answer 28

?*