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## Homework Statement

I have a sphere that I want to travel from the north pole to the south pole. The route I take is winding around the sphere (instead of the obvious shortest path). My path is dictated by:

##\phi(t)=wt##

##z(t)=R-v_z t## in the negative z direction per N to S

The form of the final answer is given!

##d_{tot}=\int_?^? A\sqrt{1+B^2sin^n(\theta)}d\theta##

A and B are some constants to find.

## Homework Equations

dl for spherical:##dl=dr\hat{r}+rd\theta \hat{\theta}+r sin(\theta)d\phi \hat{\phi}##

## The Attempt at a Solution

I know that R is constant since we're flying around at the same altitude. I believe the limits for ##\phi## are 0 to 2##\pi## and ##\theta## 0 to ##\pi##. Clearly according to the given integral I don't need to worry abut phi and R anyway though.

I thought that I may take ##z(t)=R-v_z t## and convert the z coordinate to spherical so that ##Rcos(\phi)=R-v_z t## but that hasn't really lead me anywhere near that integral so far.

Just not sure how to start. Anyone care to help point me in the right direction?