# calculus

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2. ### Retrograde motion of Mars

I have an annoying Physics question that I have been trying to work at for about 3 hours now, the class I'm taking is Calculus based but I'm not even sure if this question is necessarily calculus-related, I'm not sure how I should be approaching it. Here is a link because of the subscripts and...
3. ### Vector-based equations

I have an annoying Physics question that I have been trying to work at for about 3 hours now, the class I'm taking is Calculus based but I'm not even sure if this question is necessarily calculus-related, I'm not sure how I should be approaching it. Here is a link because of the subscripts...
4. ### snell's law and variational calculus

Working through some exercises on Variational Calculus from Taylor's Classical Mechanics. I'm not entirely sure how to set this up. I had a look at past post "http://physicshelpforum.com/advanced-optics/10876-does-fermat-principle-explain-refraction-inside-water.html" but the problem...
5. ### How do I integrate this problem?

Find the length of the curve given by the parameterization x(t)=t^4-2t^2+1 y(t)=t^2-1 on the interval 0≤t≤1 I'm stuck on the integrating the function after I put it in the curve length formula of sqrt((dx/dt)^2+(dy/dt)^2). Can anyone help?
6. ### Resistive Force Calculus Help

I have the differentialequation dv/dt = g - kv^n and need to solve it with the initial condition that v(o) = v.inital. I tried seperating the variables so i get dv = g-kv^n dt and then 1/(g-kv^n)dv = dt. Then I wanted to integrate both sides but I am not sure how or if this is even...
7. ### calculus of gravitational force

Good morning, in cases where it is not possible to neglect the extension of an irregularly shaped body as we can calculate the gravitational force exerted on the earth of it? Of course the body will be large enough that it can not consider the local Earth's field as a field of parallel forces...
8. ### I have a cumbersome problem with Vector calculus

I am unfamiliar with Vector calculus, a tool for learning Physics I select a homework I did not solve yet, then hope a help from you guys, in attachment pdf file My attempt: I tried to use BAC-CAB rule, but the key hardness of mine is I still do not know the concepts clearly (as you know a...
9. ### Quite Noob Question about IBP

Hi I integral from 0 to inf of : x*e^(-x) dx I use IBP: u = x, du = dx dv = e^(-x) dx, v = -e^(-x) uv - Int v du = -x*e^(-x) - Int -e^(-x) dx I am trying to evaluate the uv term : -x*e^(-x) from 0 to inf for the inf term of -x*e^(-x) = -inf * 1/e^(inf) = -inf * 1/inf = 1 OR -inf * 1/e^(inf)...
10. ### Acceleration, Velocity, and Position (Integral Calculus)

Note: For some reason, I am receiving a "Can't write to directory error" when I try to use LaTeX. One of the problems in my Physics textbook demands a proof of the following equation: ( v^2 - (v_0)^2 ) / 2 = integral a(s) ds from s_0 to s. The right-hand side of the equation evaluates to v(s)...
11. ### Tensor Calculus Proof

Hi, I am studying tensor calculus and I am not too familiar with tensors currently. The question I have is: The steps to prove that a lie derivative satisfies the usual product rule, ie it is Leibniz. Please see my attachment that shows where I am up to. It is much easier to scan this than...
12. ### Vector Calculus: Divergence theorem and Stokes' theorem

Hi =) I've been working on some exercises, but unfortunately we are not given the answers, so have no idea if I am going wrong or not. I attemted part a) which reads: Consider the vector field V= 3x^2y i - 2xy^2 j - xyz k Determine the divergence of this vector field and evaluate the...
13. ### Problem on Application of calculus in physics.

At a distance of 4000 ft from the launch site, a spectator is observing a rocket being launched. If the rocket lifts off vertically and is rising at a speed of 600 ft/s when it is at an altitude of 3000 ft, the distance between rocket and the spectator is changing at that instant at the rate...
14. ### A conservation and Calculus question.

Hi, I was hoping someone could offer some guidance with the following, I don't even know how to start it. The motion of a planet of mass m around the sun of mass M is governed by the following equation (note r is a vector): d^2r = -k r dt^2 ||r||^3 where K=Gm (G is the gravitational...
15. ### Integration Problem

How do integrate the indefinite integral: (x^2-3x-5)/(x+1) dx Thanks