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been having some issue with this question, mainly because it's a specific question and I don't really know where to start.

I took 12 and basically tried to find it's square root, I'm assuming newtons means speed but I don't really know, never used newtons before.

I have a book of example questions, but this isn't explained at all really, just some basic ratio examples.

also tried to use the newton measurement, but yeah, I'm stumped.

I think the question is saying a ball moving at 12 metres would have 0.2 resistance, therefore a ball with 0.1 resistance should have what, less? more?

The Air Resistance to the motion of a golf ball is proportional to the square of its speed. if the resistance to a ball moving at 12 metres per second is 0.2 Newtons, use ratios to calculate the speed of the ball when the resistance is 0.1 newtons.

any help would be appreciated.

Johnny Mccrum
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1 Answers1

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Let $R$ be the resistance. This is measured in newtons, but you don't need to know anything about that to solve this problem.

Let $v$ be the speed. This is measured in metres per second.

You want to find out the realtionship (formula) that links $R$ and $v$. In this instance they have given you some information about the type of relationship ("resistance is proportional to the square of the speed") and some data they have collected from an earlier experiment (when $v=12$, $R=0.2$).

The relationship can be expressed mathematically as $R=kv^2$

It's $v^2$ because you have been told that resistance is proportional to the square of the speed.

$k$ is called the "constant of proprtionality" and you have to use the data to find $k$ like this:

We know that when $v=12$, $R=0.2$.

Substitute these into the formula $R=kv^2$:

$0.2=k(12)^2$

$0.2=144k$

$k=\frac {0.2}{144}=\frac1{720}$

We now know that the formula is $R=\frac1{720}v^2$

Set $R=0.1$

$0.1=\frac1{720}v^2$

$72=v^2$

$v=\sqrt{72}=6\sqrt2$

tomi
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  • wait, so how would I find k then?

    the constant of proportionality? the constant is 0.2?

    no wait, R is 0.2/0.1

     – Johnny Mccrum Sep 13 '15 at 22:54
  • Substitute the known value of $R$ and the corresponding value of $v$ into the formula. – tomi Sep 13 '15 at 22:58
  • So the new R would be 0.1, right? and no idea what the v would be, don't think I have another v, right? and If I used the existing values I still have 0.2 = k12^2....unless the new v is 6, but it doesn't explicitly say that. – Johnny Mccrum Sep 13 '15 at 22:59
  • Use $R=0.2$ and $v=12$ to find a value for $k$. Use this value of $k$ and the new value of $R=0.1$ to find the bnew value of $v$. – tomi Sep 13 '15 at 23:02
  • how would I find k though? what EVEN IS k? if v is using the square, and r is the newtons, then what IS k? – Johnny Mccrum Sep 13 '15 at 23:03
  • I'll add the next step to my answer! – tomi Sep 13 '15 at 23:07
  • still so confused I think I just give up at this point, been staring at it like like an hour at this point. the answer is 8.475 and that's how you get it, but I'm still so confused, especially at the (1/720) part. – Johnny Mccrum Sep 13 '15 at 23:20