'challenging' crocodile problem (1 Viewer)

Rafy · Oct 10, 2015

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InteGrand · Oct 10, 2015

Rafy said:
http://www.bbc.com/news/uk-scotland...social&ns_campaign=bbcnews&ns_source=facebook

$Not too hard. From $\tau=\frac{D}{S}$, where $\tau$ is time, $D$ is distance, and $S$ is speed, and from Pythagoras, we can say the width of the river, $w$, is $w=6$, and $S_{\text{water}}=\frac{1}{5}$ metres per tenth-of-a-second, and $S_{\text{land}}=\frac{1}{4}$ m per tenth-of-a-second. Using Pythagoras, the shortest distance between the crocodile and zebra is $d_\text{min.}=\sqrt{36 + 20^2}=\sqrt{436}$ m. (These facts aren't even necessary to find.) Part (a) (ii) is just $T(20)$. Part a(i) is strange since it asks find the time if the crocodile does not go on land, but no path is specified; I suppose part (a) (ii)'s answer would suffice then (this is the shortest such time). The last Q. is basic calculus, not sure why it is 8 marks, unless the whole paper is out of very many marks.$

$I think part (a) (i) should have asked for $T(0)$.$

Drsoccerball · Oct 10, 2015

InteGrand said:
$Not too hard. From $\tau=\frac{D}{S}$, where $\tau$ is time, $D$ is distance, and $S$ is speed, and from Pythagoras, we can say the width of the river, $w$, is $w=6$, and $S_{\text{water}}=\frac{1}{5}$ metres per tenth-of-a-second, and $S_{\text{land}}=\frac{1}{4}$ m per tenth-of-a-second. Using Pythagoras, the shortest distance between the crocodile and zebra is $d_\text{min.}=\sqrt{36 + 20^2}=\sqrt{436}$ m. (These facts aren't even necessary to find.) Part (a) (ii) is just $T(20)$. Part a(i) is strange since it asks find the time if the crocodile does not go on land, but no path is specified; I suppose part (a) (ii)'s answer would suffice then (this is the shortest such time). The last Q. is basic calculus, not sure why it is 8 marks, unless the whole paper is out of very many marks.$

$I think part (a) (i) should have asked for $T(0)$.$

part i asked for x=20
part ii asked for x=0
part iii asked for x=2.62

InteGrand · Oct 10, 2015

Drsoccerball said:
part i asked for x=20
part ii asked for x=0
part iii asked for x=2.62

Oh right. Misinterpreted shortest distance possible as meaning "it swims the shortest distance between the croc. and zebra". It's still not a challenging Q. (Part (iii) is x = 8.)

Drsoccerball · Oct 10, 2015

InteGrand said:
Oh right. Misinterpreted shortest distance possible as meaning "it swims the shortest distance between the croc. and zebra". It's still not a challenging Q.

Why is the last question 8 marks... thats max 3

Drsoccerball · Oct 10, 2015

InteGrand said:
Oh right. Misinterpreted shortest distance possible as meaning "it swims the shortest distance between the croc. and zebra". It's still not a challenging Q.

LOL maybe that's why they thought it was challenging? everyone thought it was the shortest distance between the croc and the zebra.

InteGrand · Oct 10, 2015

Drsoccerball said:
LOL maybe that's why they thought it was challenging? everyone thought it was the shortest distance between the croc and the zebra.

Don't think that's the reason. Even if they did, that's 1 mark, the 8 mark Q. is the majority of marks, and that one's easy, because they give you the equation for time, and they even tell you that the stationary point will be a minimum, so no need to test it. The similar Q's to this that appear in the HSC here require more setting up, since they usually just tell you speeds and lengths, so you need to set up the time equation yourself.

Would be challenging if they weren't taught calculus. But they were taught it (here's the exam: http://www.sqa.org.uk/pastpapers/papers/papers/2015/NH_Mathematics_all_2015.pdf ))

Drsoccerball · Oct 10, 2015

InteGrand said:
Don't think that's the reason. Even if they did, that's 1 mark, the 8 mark Q. is the majority of marks, and that one's easy, because they give you the equation for time, and they even tell you that the stationary point will be a minimum, so no need to test it. The similar Q's to this that appear in the HSC here require more setting up, since they usually just tell you speeds and lengths, so you need to set up the time equation yourself.

Would be challenging if they weren't taught calculus.

Or algebra...

InteGrand · Oct 10, 2015

Drsoccerball said:
Or algebra...

Actually there are proofs of Snell's Law (which was essentially what this Q was about) that don't require calculus, just algebra, but they are harder to come up with (e.g. see link below):

http://www.cmi.ac.in/~debangshu/fermat.pdf

atargainz · Oct 10, 2015

dang 8 marks, that was pretty simple ...

'challenging' crocodile problem (1 Viewer)

Rafy

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InteGrand

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Drsoccerball

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InteGrand

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Drsoccerball

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InteGrand

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InteGrand

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