# Trying to solve for derivative with respect to time of vector given magnitude and two angles [closed]

I've got a problem involving dynamic vectors in which I'm being asked to find $$\dot R$$ $$\dot \theta_a$$ and $$\dot \theta_e$$

I'm given the vector of $$(R,\theta_a,\theta_e)$$ = $$(25,-120,15)$$ and $$V_{cm} = 200\hat{i} - 300\hat{j} - 100\hat{k}$$

turned the spherical coordinates into cartesian for $$R_{cm} = -5.60\hat i - 20.91\hat j - 24.14\hat k$$

The magnitude $$V = 374.16$$ with the angles $$= -56.03$$ and $$-15.5$$ in respect to the horizontal and vertical planes.

The issue I'm having is find $$\dot R$$ $$\dot \theta_a$$ and $$\dot \theta_e$$ which also known as $$\frac{dR}{dt}, \frac{d\theta_a}{dt}, and \frac{d\theta_e}{dt}$$

What I'm running into which is causing my problem is I don't see any actual variables to do any derivation to get anything other than $$\dot R = 0$$, $$\dot \theta_a = 0$$ and $$\dot \theta_e = 0$$

How would one do implicit derivation for this situation?

"Your question can be reopened if suitably edited to ask about the underlying concepts — please read the links above carefully to learn how. "

My people learn the concepts by seeing numbers and not a bunch of formulas. As an Aspie just seeing formulas gets jumbled in my head and makes no sense. Asking how to do implicit derivations for problems related to time based off physics concepts is asking a question about the underlying physics of a problem.

• Frp spherical polar coordinate, your natations are very different. from the usuaul $(r, \theta, \phi)$. What is your $\theta_a$ and $\theta_e$? – ytlu Feb 7 at 15:53
• This problem does not make sense: you can not derive simply derive a vector if you don't know what and how is changing with time. You have to write your trasnformations in symbols (R, $\theta_e$, etc.), decide what depends on time (R(t)? $\theta_e(t)$?) and then carry out the derivatives (there will be composite products so you need the chain rule etc.). But then you need to know the function $R(t)$ or $\theta_e(t)$ to solve it completely.. – JalfredP Feb 7 at 16:32
• @ ytlu the first angle is theta azimuth, and the second is theta elevation. @JalfredP that's the issue. This is how I am constantly running up again when ever asked for a derivative with respect to time. I'm never given actual variables to derive. Yet I'm the only one in my class it seems that simple doesn't get it. – David Scidmore Feb 7 at 16:45

## 1 Answer

You can get expressions for x,y, and z in terms of polar coordinates. Take the derivative of each of these with respect to time (in terms of dR/dt and dθ/dt). You know the values of the radius, sines and cosines. From the given velocity, you also know the values of the derivatives (of x,y, and z). That gives you three equations which you can solve for your three unknowns.