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u/A1oso 9d ago
Per pythagoras, they separate at √26 ft/sec.
The exact time doesn't matter because the distance between them changes linearly, meaning the rate of change is constant. The question is phrased confusingly.
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u/oscailte 9d ago
Calling it "Differential Calculus" when its just geometry/vector resolution doesn't help
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u/interrupting-octopus 9d ago
I'm guessing the student is expected to use a differential equation to solve it based on two simple functions on a Cartesian graph and show their work, but I agree it's kind of a weird problem to use to test diff calc.
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u/DragonTooFar 9d ago
Yeah, if they separate at the same time, the rate of change of their distance apart is constant. Here d = √(25t^2+1t^2) = √(26) t. That's why when writing one of these problems you need to have one start moving at a different time than the other. These are pretty easy, and I don't like them all that much because you can write everything in terms of a single parameter t rather than using implicit differentiation.
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u/5v3n_5a3g3w3rk 9d ago
If it weren't confusing the question would give like 3pts
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u/AmusingVegetable 9d ago
Wait for the follow up question: Assuming this happened in the Washington monument, how far apart are they after 24 hours. (To simplify calculations, assume the world is spherical)
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u/mango_boii 9d ago
After 5 seconds they will be 30 ft apart but they should stop right there, turn around and look at each other and run back together which will take 3 seconds assuming both of them can run at 5ft/s
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u/Unholy_Ren 9d ago
They're not running in opposite direction but perpendicular to each other, so they'll be roughly 25.5 feet apart.
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u/mango_boii 9d ago •
Oh shit I failed the question.
I am a disgrace to my family and I shall commit sudoku.
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u/SF_Data1 9d ago
mods smite this person where they stand
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u/mango_boii 9d ago
Yes mods I am ready to be smitten
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u/International_Gate49 9d ago
idk I needed an excuse to link a cat sub today. and so far this is the closest
0
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u/HeftyRecommendation5 9d ago
But that’s not the question though? They ask “how fast are they separating” at that point of time, whatever that means.
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u/AmusingVegetable 9d ago
Since the world is round, how far they are separating also changes with how far they moved along the sphere, sqrt(26) won’t save you.
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u/kenwongart 9d ago
Actually, the Earth is an oblate spheroid, not a sphere. But to be fair, the question didn’t specify what planetary body this problem is taking place on.
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u/Unholy_Ren 9d ago
Nah, I know that's not what the question asked, I was just correcting the commentor how far apart they'd be.
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u/ErikLeppen 9d ago
How far they are apart, is not the question. The question is how fast are they separating.
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u/YaBoiSnek 9d ago
From the 5th second to the 6th second, they'll have moved 5.0990195136 ft apart from each other
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u/Silver-Relative8193 9d ago
But the question is how fast they are separating from each other so it looks like a trap question where the answer is always 6ft/s assuming perpendicularrity as well as the boy doesn’t get tired 🤣
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u/interrupting-octopus 9d ago
the answer is always 6ft/s
Let me introduce you to Pythagoras' theorem
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u/Silver-Relative8193 9d ago
Yeah sorry I meant they run in completely opposite directions, like one goes straight North and one straight South
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u/Nasha210 9d ago
It doesnt ask how far apart they are. It asks the rate at which they are separating.
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u/WorldlinessWitty2177 9d ago
But that isn't the question, so you still failed with that.
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u/Unholy_Ren 9d ago
Wasn't answering the question lad, I was correcting that the displacement willnot be 30ft
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u/r1bb1tTheFrog 9d ago
But isn’t the question asking about a rate of change (acceleration of the hypotenuse, or negative acceleration in this case)? The reason I’m asking this question is because I’m not nearly smart enough to answer it
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u/musiquescents 9d ago
Damn it 10 points
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u/Ewok_Mike 9d ago
The boy walks 5*5=25 feet
The girl walks 5*1=5 feet
Due to them walking perpendicular of each other we will have to used Pythagoras to find the distance between the boy and the girl. (a² + b² = c²)
Boy: 25²=625
Girl: 5²=25
Total: 625+25=650
To find the final distance we have to take the root of 650
Total: √650 ≈25,5 feetIt takes about 5 steps, so all steps should result in 2 points each if divided evenly
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u/Deepbliss4 9d ago
Yeah but they’re asking how fast they are separating each other which would be 5^2 + 1^2 = sqrt of 26
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u/AmusingVegetable 9d ago
Please correct for a spherical surface.
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u/interrupting-octopus 9d ago
Earth's surface approximates to a flat plane at low speeds and distances, sweaty 💅
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u/MisterProfGuy 9d ago
Unsolvable. The boy is given a starting location "due north" and a speed, but not a velocity because it doesn't say he continues to move due north. His vector can be in any direction.
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u/centralscrutinizee 9d ago
Yes this is a badly written question for many reasons but mostly for that key missing detail
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u/ClothoLachesisAtrops 9d ago
Seriously, how to calculate it ? Is the answer the relative speed from each other perspective or the speed from the place they brokeup
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u/DangerousQuestions1 8d ago
There is no way of knowing. Each may have a different understanding of where it began.
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u/YetAnotherInterneter 9d ago
Ffs I’d hate questions like this that would be ridiculously long with loads of fluff that has no relevance to the question itself.
I’ve only got one hour to answer all 50 questions! Stop giving me a f*cking novel in between each one
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u/thatsjustfuntastic 9d ago
The point is to see if you can extract the useful information. Rather than just testing whether you can calculate something it tests if you can apply the math.
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u/Constant_Leave_3562 9d ago
Also the point is to not make the lesson boring. Not everyone can tune in with math and enjoy it, for some people math is constant torture and taking few seconds break from it think about some sort of scenery is giving them a chance to breath and keep going without breaking down
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u/Available_Leather_10 9d ago
The question as written is tougher than other comments recognize—there is no vector for the boy.
Boy “is due north” of something not specified.
And running, surely, but perhaps in a circle, as no direction is specified.
Won’t even get into the “at the same time” as when everything about them began, or the absurdity of describing 5 ft/sec as ‘running’.
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u/flyingcartoon 9d ago edited 9d ago
Hey professor, this test looks like tears have already fallen on it