Recent content by Steely Dan

You've made an algebraic mistake in your part b), but yes, you are on the right track. By the way, a thread like this belongs in the "Introductory Physics" forum, not the Calculus forum.

I didn't use the word direction, and I'm not disputing that the force vector (or displacement vector) always points in a direction between the two bodies. But a given vector that points between the two bodies will have different components if you (for example) rotate your coordinate system by 30...

When I first looked at it I assumed you had calculated the coefficients incorrectly, but I just took another look at it and maybe I was wrong. I'll take a closer look later on. The negative sign in the recursion relation definitely worries me; it shouldn't be there, I think.

Force is a vector quantity. The vector's components do in fact change depending on the coordinate system. What you are saying (and what is true) is that the magnitude of the force (which is a scalar quantity) does not change from coordinate system to coordinate system. The same is true for the...

The best simple and qualitative explanation I've heard about this is to imagine that we are always traveling through space-time at the speed of light, c. That is, motion through both space and time has to add up to that number, so motion through space slows down your motion through time, and...

That is still problematic, because the sine function will always have zeros at some locations, so it doesn't satisfy the requirement that the function must be strictly positive.

This doesn't work. Multiplying by B on the right leaves ones on the first column, whereas multiplying by B on the left leaves ones on the first row.

Everything up until here is correct, as far as I can tell (you went to the trouble of posting everything, even though it's not exactly what I was asking for, so I tried to follow everything as best as I could). There is an error here, however. What you have actually written down is the...

This just in: the IAU votes to reverse its 2006 decision, and adds Eris to the list of planets as well, citing a need for our solar system to remain on top.

Does that not affect the answer? If every part of the curve must cover some area, my intuition says the total area covered must be infinite. You could make it oscillate fast enough so that the function is effectively equal to some \epsilon > 0 for all x, but the integral of that constant small...

I didn't mean it like that all! It's only obvious to the physicist after you've had some practice with it (which you're now starting to get). One of the great things about being an undergrad is that you do it the hard way now, so that you can justify doing it the easy way for the rest of your...

Yes, that's the idea. Conservation of momentum dictates m_1 v_1 = m_2 v_4, solving for the initial speed is just an algebra problem.

Correct.

The speed of light through any particular medium is usually written as c / n, where n is the index of refraction of the medium.

I think that solving nine simultaneous equations is pretty "lame." Finding simple answers to problems that seem complicated is what is cool. But I don't know what the authors were looking for. That depends on whether they're the type of author that has a sense of humor or not.