Trig Help

[V|P]

I got a riddle type question for bonus points in Trig on Thursday. I have until tommorow to solve it, and I just can't figure it out. I already put it on Yahoo Answers, but I thought this audience would be more of a help. Anyway, here's the question:

A car's wheel (with tire) is 26 inches in diameter and its center is 12 inches above the road. If the car is traveling at 60 feet per second, how fast is the highest point of the tire moving relative to the ground?

An answer is appreciated, but I'd really rather have a step-by-step walkthrough on HOW to do it, since this will eventually come up in physics also. I attached the scan.

[shwaip]

so, do you deserve the bonus points if you can't figure it out?

[V|P]

so, do you deserve the bonus points if you can't figure it out?
Well I guess that depends on the way you look at it. If you've been in High School you know that one person will get the answer from some professional mathematician or something they know and everyone else will copy of off them. Anyway, you don't have to help. I'm still trying to figure it out, and if I don't get it I just won't get the points, but I'm not losing anything so... It's two points in case you're wondering.

[Thrax]

I think there's only one way to look at it: You get the bonus points if you're clever enough to do it on your own. So happens other people might cheat -- that's their own moral slippery slope.

Do you want to join them?

[Guyute]

I am wondering how a tire we assume is round can have a radius of 12 and a diameter of 26? I know in the real world the tire is compressed...

[V|P]

I am wondering how a tire we assume is round can have a radius of 12 and a diameter of 26? I know in the real world the tire is compressed...

The wheel without the tire has a radius of 12. With the tire, the diameter would be 26, meaning the tire is 1'' thick.

[shwaip]

I am wondering how a tire we assume is round can have a radius of 12 and a diameter of 26? I know in the real world the tire is compressed...

you win so hard.

[drasnor]

Hint: how fast (linear) is the part of the tire in contact with the road moving relative to the road? How about the axle?

-drasnor :fold:

[airbornflght]

This doesn't seem that hard to me.


But, I kind of feel sorry for you. I haven't taken math in a a year and a half and I got thrown into Calc 2014...not good. I was studying last night and everything started making sense. At least limits. Now onto derivatives. They did say most engineers are pre-business.

[drasnor]

This doesn't seem that hard to me.It's a classic introductory dynamics problem. Everyone I know in engineering including myself has seen this on an exam before. The only hard part here is identifying the problem.

-drasnor :fold:

[V|P]

It's a classic introductory dynamics problem. Everyone I know in engineering including myself has seen this on an exam before. The only hard part here is identifying the problem.

-drasnor :fold:

Thanks for the hint. Amazingly, that was really all I needed even though you were slightly to late. I'm not exactly sure of how, but I did solve it this morning before class but I couldn't explain my thought process. Hopefully I'll still get the points since I did show all my work. I tend to get myself in this situation a lot. Especially in Physics this year, I seem to be able to sovle 99% of the problems on our tests/homework, but when they ask me to explain how I did it, I hit a road block. I don't have a problem in English class and I admit my grammar and vocabulary aren't the greatest in the world, but explaining math and science problems really gets me.

In my eyes, if you can solve it, you win. Even if you don't show work but you get the right answer, why should teachers care in high school. I mean if we used a calculator program to do our work isn't that our loss?

[bothered]

A car's wheel (with tire) is 26 inches in diameter and its center is 12 inches above the road.

The wheel without the tire has a radius of 12. With the tire, the diameter would be 26, meaning the tire is 1'' thick.

So which is it? There is nothing in the question that suggests how thick the tire is, nor does it matter. Only road to axle=12, axle to top of tire=14. And, if the wheel is has a radius of 12 then there is no tire between the wheel and the road???

[V|P]

So which is it? There is nothing in the question that suggests how thick the tire is, nor does it matter. Only road to axle=12, axle to top of tire=14. And, if the wheel is has a radius of 12 then there is no tire between the wheel and the road???

Look at the picture I attached.

[lightnin]

In my eyes, if you can solve it, you win. Even if you don't show work but you get the right answer, why should teachers care in high school. I mean if we used a calculator program to do our work isn't that our loss?

not to nag you but...

because accurate results are reproducible. how do we know you didn't just coincidently arrive at the proper conclusion?

what happens when you have to work backwards or make a proof of a theorem?

the earlier you learn best practices of *any* field the better off you are in the long run. IMNSHO calculators should absolutely be BANNED from use in classes unless the instructor is teaching you simply how to use the calculator, not how to do math.

[Guyute]

Ahh, my bad- the diagram does show the extra radius. Good point- "RTFQ", right?!?! hehe

I had many math classes whereby they insisted on showing work. Avoids cheating, I was told.

[V|P]

I had many math classes whereby they insisted on showing work. Avoids cheating, I was told.

That's what I'm saying though. The teachers go on and on about how they don't care about you at all, yet they care if you might have cheated. Isn't that your problem if you don't know how to do something. Why do they care?

And I don't have problem showing work. I just have a problem explaining it in essay form...

[drasnor]

Calculators are useful for rapid computation. If you don't understand the theory upon which the computation is based you won't know the limitations of the computation being performed. This is especially true when you start trying to solve complex problems with your calculator. It becomes important to know what algorithm the calculator is using so that you know if it is suitable for your application.

-drasnor :fold:

[V|P]

Calculators are useful for rapid computation. If you don't understand the theory upon which the computation is based you won't know the limitations of the computation being performed. This is especially true when you start trying to solve complex problems with your calculator. It becomes important to know what algorithm the calculator is using so that you know if it is suitable for your application.

-drasnor :fold:

I'll try to say this once again. Either I can't type for crap or you guys really aren't reading my whole posts. I don't mind learning the math and showing my work, I just hate putting it into essay form or explaining it. I've tried tutoring kids in Math, and I know how to do it perfectly, and yet I can't teach it properly because it's just really hard for me to explain the way I think mathematically.

This leads me to another problem. When teachers tell me how to do a problem I hate it. It's okay if the test is on a certain concept they're teaching, but when we're past that concept and I choose to solve a problem a different way, what's the difference. I tend to think differently mathematically than most people. For example, if I had to multiply two numbers like, say, 1257 x 8, I tend to do it in my head by first multiplying 1000 by 8, adding 200 x 8, adding 50 x 8, and adding 7 x 8. This seems long a tedious and sometimes doesn't work out on paper, but it ends up being right and in my head it just makes sense. To explain algebra concepts in random ways like this, it get really difficult.

...

[jokke]

I tend to think differently mathematically than most people. For example, if I had to multiply two numbers like, say, 1257 x 8, I tend to do it in my head by first multiplying 1000 by 8, adding 200 x 8, adding 50 x 8, and adding 7 x 8. This seems long a tedious and sometimes doesn't work out on paper, but it ends up being right and in my head it just makes sense.

I think exactly the same way! It may sound weird, but it really works, and it's really quite easy!

[V|P]

Not sure why you quoted that....

[shwaip]

For example, if I had to multiply two numbers like, say, 1257 x 8, I tend to do it in my head by first multiplying 1000 by 8, adding 200 x 8, adding 50 x 8, and adding 7 x 8. This seems long a tedious and sometimes doesn't work out on paper, but it ends up being right and in my head it just makes sense. To explain algebra concepts in random ways like this, it get really difficult.

...

this is how you do multiplication on paper...

As far as the "essay" part, this is actually the best way to see if you actually understand something. I always thought that I knew how to do signal processing, then I had to TA for a quarter, and the questions that they asked showed me I didn't really know all the stuff i thought i did.

[V|P]

As far as the "essay" part, this is actually the best way to see if you actually understand something.

But if you can solve it, you must understand it right? I mean seriously solve it not copy...

[Nomad]

But if you can solve it, you must understand it right? I mean seriously solve it not copy...

How do you show that you haven't copied?

[V|P]

How do you show that you haven't copied?

Why do they care?

Anyway that's not the point. What I'm saying is that you must have understood it if you were able to solve it without copying. (Let's pretend you were in an isolated room with no one but the teacher and yourself, the question will still ask me to explain in essay form right, but since there's no one there, I had to have solved it myself...)

[Nomad]

Why do they care?

oh i don't know something about integrity

[csimon]

I dont get it ...so you travel on a partially flat tire at 600ft per sec. Everything is travelling at the same rate ...you, the tire, the rest of the car ...etc. Wouldn't the top of the tire be travelling at this rate?
What am I missing here and what does it have to do with trig?

[drasnor]

I dont get it ...so you travel on a partially flat tire at 600ft per sec. Everything is travelling at the same rate ...you, the tire, the rest of the car ...etc. Wouldn't the top of the tire be travelling at this rate?
What am I missing here and what does it have to do with trig?Not quite. The tire is spinning about the axle which makes the car move at 60 ft/sec. However, the tire doesn't slip against the ground unless you're in a skid. As a result, if you take a snapshot of the car's motion then the car and axle will be translating horizontally at 60 ft/sec while the contact patch won't be moving at all. From here it's just a similar triangles problem:

-drasnor :fold:

P.S. There's an ongoing debate as to the geometry of the problem. Either the tire maintains a constant diameter of 26" and the axle is offset down 1" or the tire deforms to where the radius is typically 13" except for the 12" deformed area in contact with the pavement. It's subject to interpretation but the methodology for solving either case is the same. Another reason it's important to show your work is so you can whore for partial credit later if you pick the wrong interpretation of an ambiguously-worded problem.

[Leonardo]

so you travel on a partially flat tire at 600ft per sec350MPH on an improperly inflated tire? NO THANK YOU! :eek:

[V|P]

I don't want to revive this thread for it's original point, but I mentioned earlier somewhere that I did math differently. I couldn't give a proper example at the time, but today in a Physics test, I had a problem that I did very differently from everyone else, and ended up getting one more sig fig than everyone else. I initially lost a point for incorrect sig figs, but when I explained the problem to my teacher, he gave the point back to me. So here's the problem (I don't remember it EXACTLY):

You have something or other going at 2.50 m/s for 15.0 minutes. Then, it slows down and it goes 2.20 m/s for 1,320 m. What is the average velocity?

I know this is a simple problem, but it is a review from last year, and this test only had 3 problems, so I can't really give you a better example. Anyway, this is how I did it:


1) First I converted 1320 m to amount of time in seconds (600 s). So all my numbers have 3 sig figs at this point.

2) I then divided 900 by 300 and 600 by 300. I got 3.00 and 2.00 respectively, and so I still have 3 sig figs in all my numbers.

3) I multiplied 2.50 x 3 to get 7.50 and 2.20 x 2 to get 4.40. (Still three sig figs).

4) I added 7.50 + 4.40 to get 11.90. (4 sig figs now.)

5) I divided 11.90 / 5 and got 2.380 m/s. (Still 4 sig figs).


Also like I mentioned before, my way seems like it's a lot more work than conventional methods, but when you look at it on paper, its less than half the work. So if you did this same problem by equation, you end you with 3 sig figs rather than 4.

In physics, it's okay for me to do problems like this because my teacher tends to go by "If you answered the question and showed me how you did it, you get the points." He suggests the best ways to do something, and if we prefer to do it a different way, he doesn't care. These are the kinds of teachers we need.

BTW, our physics teacher read this story to us the first day of school:
http://philosophy.lander.edu/intro/introbook2.1/x874.html

[jokke]

Wow, that story is awsome. Really makes you think.

[shwaip]

you shouldn't have gotten that point. your last division is:

11.90 / 5.00 = 2.38

[V|P]

5 is an exact number. Infinite sig figs. If you're wondering where I got it, look at step 3. Add the 3 and the 2, both exact numbers.

[shwaip]

where did you get the numbers for step 3?

[V|P]

where did you get the numbers for step 3?

This is what I mean. It's really hard for me to explain to you where I got them. It's just the way I thought of it...

EDIT:
I'm sorry SHWAIP, I looked at it wrong. The way I put it, I shouldn't have gotten that point. I just looked and realized I forgot to take into consideration 600 and 900 s into sig figs... I'll have to take a look at my test on Tuesday to see if I wrote the problem wrong or if I really didn't deserve that point...