Is this question worded poorly? (Limiting sum) (1 Viewer)

[BlueGas]

A ball is dropped 12 metres onto a flat surface, rebounds 9 metres and continues to bounce to 3/4 of its previous height. If it is allowed to bounce until it stops, through what total distance does it travel?

Now I knew how to work out this questions after I looked at a different example from a different textbook. But what made me confused for this question is that I thought they wanted me to find the 'sum of the total distance it traveled from 12 metres until it fully stopped bouncing', well that's what the questions says anyway: " to bounce until it stops", is the question worded poorly or is it just me?

 

[InteGrand]

A ball is dropped 12 metres onto a flat surface, rebounds 9 metres and continues to bounce to 3/4 of its previous height. If it is allowed to bounce until it stops, through what total distance does it travel?

Now I knew how to work out this questions after I looked at a different example from a different textbook. But what made me confused for this question is that I thought they wanted me to find the 'sum of the total distance it traveled from 12 metres until it fully stopped bouncing', well that's what the questions says anyway: " to bounce until it stops", is the question worded poorly or is it just me?

That is what it wants (an infinite GP sum).

 

[BlueGas]

That is what it wants (an infinite GP sum).

Well how about this question: The height of a tree was 10 metres and it increased by 2 metres during the next year. If in each succeeding year the growth is 2/3 of that in the previous year, find the limiting height.

How would you work out this question? It doesn't even make sense, if the first year was 10 metres, the next year should be 12 metres because it 'increased' by 2 metres. 2/3 of 12 doesn't give 10, it gives you 8. This questions is confusing.

 

[enigma_1]

Lol these are definitely mif questions

Don't bother

 

[BlueGas]

Lol these are definitely mif questions

Don't bother

I was actually expecting you, that's why I wanted to put in my original post, "not from MIF", haha, but these questions are from Jones and Couchman. I actually sometimes feel like I'm answering MIF questions when I answer questions from Jones and Couchman, I also use Fitpatrick's book when there are times Jones and Couchman don't explain their examples properly.

 

[enigma_1]

I was actually expecting you, that's why I wanted to put in my original post, "not from MIF", haha, but these questions are from Jones and Couchman. I actually sometimes feel like I'm answering MIF questions when I answer questions from Jones and Couchman, I also use Fitpatrick's book when there are times Jones and Couchman don't explain their examples properly.

Lmao wow that's like mif level questions.

Jones and couchman is like on the same level as mif but maybe "slightly" better I guess.

 

[InteGrand]

Well how about this question: The height of a tree was 10 metres and it increased by 2 metres during the next year. If in each succeeding year the growth is 2/3 of that in the previous year, find the limiting height.

How would you work out this question? It doesn't even make sense, if the first year was 10 metres, the next year should be 12 metres because it 'increased' by 2 metres. 2/3 of 12 doesn't give 10, it gives you 8. This questions is confusing.

The question means that the first growth was of 2 m, and then each successive growth was ⅔ the previous growth, so the growth amounts form a GP with starting term of and common ratio .

 

[BlueGas]

The question means that the first growth was of 2 m, and then each successive growth was ⅔ the previous growth, so the growth amounts form a GP with starting term of and common ratio .

So what do you get as an answer?

 

[InteGrand]

So what do you get as an answer?

I haven't done it, but we just need to use the limiting sum of a GP formula to find the total growth and add this to the initial height to find the limiting height.

 

[BlueGas]

I haven't done it, but we just need to use the limiting sum of a GP formula to find the total growth and add this to the initial height to find the limiting height.

Ah so that's how you get a final answer of 16, 6 (limiting sum) + 10 (initial height), this question is quite tricky.

 

[D94]

Well how about this question: The height of a tree was 10 metres and it increased by 2 metres during the next year. If in each succeeding year the growth is 2/3 of that in the previous year, find the limiting height.

How would you work out this question? It doesn't even make sense, if the first year was 10 metres, the next year should be 12 metres because it 'increased' by 2 metres. 2/3 of 12 doesn't give 10, it gives you 8. This questions is confusing.

What's so confusing about it? I haven't done these in 4 years but it's obvious that it starts off as 10m, then in the first year it grows by 2m to become 12m, then every year after that, it increases 2/3 of the difference between the last two years, i.e. 2/3 of 2, then 2/3 of (2/3 of 2), and so on.

The "of that" means growth, not the total height. That sentence makes no reference to total height prior to 2/3, so it cannot possibly be referring to total height.