call smart math pplz

[paradise!]

All right, well i've got 3 questions, but here's one.

1) You are videotaping a race from a stand 132 ft from the track, following a car that is moving 264ft/sec. How fast will your camera angle (theta) be changing when the car is in front of you.

Ok heres what i have so far:
dx/dt= -264 ft/sec
at x=0
y=132

Ok so i know i have to create a relationship, so...:
x^2(haha phizey) + 132 = z^2
xdx/dt+ydy/dt=zdz/dt // now i will substitute

So i get like z*dz/dt=0, what the fuck? // since im looking for x=0

Then i was thinking this..just friggin input dx/dt as the length of x (to find theta).
tan theta = 264/132. So i get theta=63.43
But the answer is 2 radians, and im getting 2 radians right here. But this can't be the right way.
I know i have to differentiate implicitly for time, so i get like

so I know tan theta= y/x
y=132, so 132tan(theta)=1/x
differentiate:
132sec^2(theta)*dtheta/dt=1/x^2*dx/dt
WOULD I PLUG THETA BACK IN? QUESTION MARK QUESTION MARK

[Zeebu]

stop making it so hard

if i understand this right, you are looking for rad/s

how many rad/s is your camera goin at the point where the car is 132 ft away from you going 264 ft/s

hint: radians dont really have units

[paradise!]

stop making it so hard

if i understand this right, you are looking for rad/s

how many rad/s is your camera goin at the point where the car is 132 ft away from you going 264 ft/s

hint: radians dont really have units

what the hell?

[Zeebu]

is the problem only asking for what you want at that exact time or is it asking for an equation for any time?


edit: are you looking for 2 rad/s CCW? or are you looking for an equation for rad/s at any time?

[paradise!]

is the problem only asking for what you want at that exact time or is it asking for an equation for any time?

its asking how fast is the angle changing when it is directly under me, which i assumed is x=0.

I just don't get it.

[Zeebu]

then all you need to do is divide 264 by 132.


lets say its a straight track

you are 132 ft away from the track.

when the car passes right across from you going 264 ft/s how fast would you need to be turing your camera to keep it pointed at the car


use your units.

you are looking for something in rad/s


264 ft/s divided by 132 ft

divide it out and you get 1/s which is what you want

[paradise!]

holy crap thanks. Completely over thought that.

When im thinking about it. Why can't it be 1 radian per second. If i am standing in a tower, don't i have to match the speed of the car? Thus the camera needs to be turning at 264 ft pr second. Or maybe it is in the trig relation. for 264/132

..is there anyway you can show me this mathematically.

theta would be zero right? and x=0? anyway i can show this relationship with math?

[Money]

how u gonna learn when u come here for answers???????????????????????????????????????

what was it again? Harvard or Stanford? LOL

[paradise!]

smoke weed

----------

I've figured it out, thanks zee.

[Money]

harvard or yale?

[Vykromond]

he's right though i mean you can cheat off other people for a pretty long time even in college but it's not actually a good idea to go to a top school if you can't hack the work, you won't be particularly happy and you won't learn (because the work will be above your head)

so it'd basically be a waste of an asston of money unless you can finagle a full scholarship or something

[Galleleo]

If you are talking about the exact moment the car is under you at 132 ft away from your camera. The camera is not moving at all? That exact moment it is pointed straight down (or ahead) at the car that is exactly right in front of you.

[Stompa]

hey para i just got into johns hopkins

[DankNuggets]

A. Is this a blackboard/CAPA question? If so, shouldn't you get an assload of guesses? Then using logic, if you see the values 264, and 132, wouldn't you immediately start guessing things like .25, .5, 1, 2, 4 ..... i mean i'm good at math and physics, but when it comes to stupid CAPA problems I usually just guess to save me time.


B. If this is regular homework, why not get a classmate to help you? or the teacher? that way they can actually explain it one on one. You're going to get very little out of anything we give you, even if it's spelled out perfectly.


C. If this is an exam question, you'd defintely want to get help from an IRL person who can help you show the work. Putting down an answer that's possibly very wrong with no or incorrect work might tip your prof off that you're cheating.


all this being said, i'll post what i think the solution is so you can actually learn it (if im right)

[DankNuggets]

if that's the correct problem then i'd do it this way.

First, write out your two equations:

x = 264*t (x is horz distance along track in ft, t is time in secs)
θ= tan(x/132)

substitute for x

θ=tan(264t/132)
θ=tan(2t)

now take the dervitive to find dθ/dt, the rate at which θ is changing.

dθ/dt=2sec^2(2t) or =2/(cos^2(2t))

evaluate at which ever time, t, you want.

i think there was probably more to the problem, and i'm probably overlooking some missing information. i'm thinking there should be a starting t value, as well as a particular point on the track. If you're in the curve, the angle will change much slower than if you were in a flat section.

evaluating that equation for t=0, gives you 2/(cos^2(0) --> 2/1 --> 2.

brings me back to my previous suggestion of just guessing obvious numbers.