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Datsyuk4242 said:
Hmmm, just wondering if anyone could help me work out a little math problem. I calculated an answer that was ultimately different than what the textbook had, so it'd be great if I got a second opinion.


The members of a high school bastketball team are driving from Calgary to Vancouver, which is a distance of 675km. Each tire on their van has a radius of 32 cm. If the team members drive at a constant speed and cover the distance from Calgary to Vancouver in 6 H 45 min, what is the angular velocity, in radians/sec, of each tire during the drive?


Please and thank you :)
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Alright, I'll try my best :)

Just to make sure everything is in the same units, I would recommend changing the distance and radius into meters, and the 6H 45 min into seconds, the standard SI units.

So, you have 675,000m, and the radius of the tires are .32m. The van covers 675,000m in 24,300 seconds. Let's find the average RPM, revolutions per minute. How many times does the tire have to rotate to get to Vancouver? The distance divided by the circumference of the tire, right? As the circumference of the tire is .64π, or 2.011m, the number of revolutions is 335,653.904. We know the entire trip takes 24300 seconds, or 405 minutes, so the Revolutions per Minute = 828.775RPM. Now, to convert RPM to rad/s, here are the steps (R = revolutions, rad = radians)
1R/m = 2πrad/m = 2πrad/60s = πrad/30s. 1 RPM = πrad/30s. Therefore, you do (828.775 * π)rad/30s. So, the answer is 86.787 rad/s.
 
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MatthewGor123 said:
Alright, I'll try my best :)

Just to make sure everything is in the same units, I would recommend changing the distance and radius into meters, and the 6H 45 min into seconds, the standard SI units.

So, you have 675,000m, and the radius of the tires are .32m. The van covers 675,000m in 24,300 seconds. Let's find the average RPM, revolutions per minute. How many times does the tire have to rotate to get to Vancouver? The distance divided by the circumference of the tire, right? As the circumference of the tire is .64π, or 2.011m, the number of revolutions is 335,653.904. We know the entire trip takes 24300 seconds, or 405 minutes, so the Revolutions per Minute = 828.775RPM. Now, to convert RPM to rad/s, here are the steps (R = revolutions, rad = radians)
1R/m = 2πrad/m = 2πrad/60s = πrad/30s. 1 RPM = πrad/30s. Therefore, you do (828.775 * π)rad/30s. So, the answer is 86.787 rad/s.
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Yep, I got the same answer. The book said 144.5 rad/s but I think that it's just a publishing error.
 
Datsyuk4242 said:
Yep, I got the same answer. The book said 144.5 rad/s but I think that it's just a publishing error.
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Either that or we're both making the same error :O (or maybe the question is phrased differently?) Just out of curiosity (as I took Physics last year), which textbook are you guys using?
 
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Its actually a math textbook, Nelson Advanced Functions (First Edition).
The book itself actually has a lot of errors in it, being the first edition and all the publishers probably hurried the distribution process.
 
you can help by not double posting xD. Had a trig test today I think I failed dumb identities
I hate them
 
Dang.. Coulda used you last year lol. Ntl, I'll probably hit you up soon. Do you understand like chemistry equations and stuff?
 
Range Me said:
yo dude ty for the math help on my thread. I'll prob post another problem later for ya. I think i understand it now..
Click to expand...

My pleasure :) Glad you understand it.

You factored incorrectly in your very first step.

ax + x - 5a - 5 = (a+1)x - 5(a+1), not (a-1). That's because when you distribute a negative (-5) over a positive (+1), you end up with -5, which is what you want.

The denominator was also incorrect;
ax - x - 5a + 5 = (a-1)x - 5(a-1), not (a+1), because when you distribute a negative (-5) over a negative (-1), you get a positive (+5).

So, you should have:
(a+1)x - 5(a+1)
(a-1)x - 5(a-1).

From here, we can do some further factoring -
(a+1)(x-5)
(a-1)(x-5)

If this step is unclear, you can rename (for the numerator) the expression (a+1) as z, and it should be more clear. If you have z*x - 5*z, which is factored as z(x-5). Then, you just plug back (a+1) for z, and this step makes sense. The same is done for the numerator.

Of course, you see (x-5) in the numerator and denominator, and those cancel out, leaving you simply:
(a+1)
(a-1)
Click to expand...

The_Void said:
Dang.. Coulda used you last year lol. Ntl, I'll probably hit you up soon. Do you understand like chemistry equations and stuff?
Click to expand...

Chemistry is probably my worst of the basic sciences :( I'm fine at bio, good at physics, and pretty shitty at chem. All I know about chem is what we learned in bio in my summer college class, and in my bio class for high school this year. I guess I understand some ionization/polarity, some basic structural formulas, w/e. Post and if you want, add me on MSN, and I can try to help :) But don't be sad if I can't :(
 
Koot said:
Did you learn integration yet? I'm currently up to there and a bit stuck.

Integral of (tan^2 y + 1)dy
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Nope; algebraic manipulation I'm fine with, but I munch at integration :( Pre-calc, fine. But ugh, sorry. A friend of mine, Unb4nn3d, will probably be able to help you out though. [maybe, possibly]. The stuff I know, I'm good at. The stuff I don't, I can't really help :P

Sorry mate :(. My dad's in Switzerland, not getting back 'till Friday afternoon, and by then it'll probably be too late, and my grandpa can't help me (he usually helps me with nubby calculus if I have questions) atm because he's in the hospital so...sorry :'(

IFAIL.
 
Koot said:
Ah it's alright I'll use ask my teacher.

I'm not sure unb4nn3d can do it since hes taking pre-cal and gonna take calculus soon.
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He said he'll ask his teacher tomorrow, and get back to you [or anyways, he said he'll try]. Hope you get the answer you're looking for :D
 
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