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For problem: See Attachment
I've never done a problem of this sort and it's proving to be much more difficult compared to the other problems I have had assigned to me.
I'm not entirely sure which formulas to use but I've been playing with the following:
Length of Arc = r[itex]\theta[/itex]
A = [itex]\pi[/itex]r^2
C = [itex]\pi[/itex]d = 2[itex]\pi[/itex]r
A of Sector= 1/2([itex]\theta[/itex]Sin[itex]\theta[/itex])r^2
And the Cosine Law
Being honest, I'm a little confused by the question. I'm not entirely sure if I labelled my variables correctly. But I made a diagram and this is what I did so far:
 L = r[itex]\theta[/itex]
So: dL/dt = dr/dt x d[itex]\theta[/itex]/dt
I assumed the walking speed on the surface was dL/dt. Therefore, dL/dt = 4.
I assumed d[itex]\theta[/itex]/dt = 4 m/s x 2[itex]\pi[/itex] rad/m = 8.
Therefore, I was able to calculate that dr/dt = 1/2.
I differentiated the cosine formula just to give myself a general idea of what I had to work with, but with two variable side lengths and an unknown [itex]\theta[/itex] I was at a loss.
Note: After quite a bit of searching, this was the closest value I found to help me out.
But in this example, a value for theta is given and two side lengths are known.
I think my main problem may be understanding the question. If someone could clarify it and give me some pointers that would be great!
Thanks!
I've never done a problem of this sort and it's proving to be much more difficult compared to the other problems I have had assigned to me.
I'm not entirely sure which formulas to use but I've been playing with the following:
Length of Arc = r[itex]\theta[/itex]
A = [itex]\pi[/itex]r^2
C = [itex]\pi[/itex]d = 2[itex]\pi[/itex]r
A of Sector= 1/2([itex]\theta[/itex]Sin[itex]\theta[/itex])r^2
And the Cosine Law
Being honest, I'm a little confused by the question. I'm not entirely sure if I labelled my variables correctly. But I made a diagram and this is what I did so far:
 L = r[itex]\theta[/itex]
So: dL/dt = dr/dt x d[itex]\theta[/itex]/dt
I assumed the walking speed on the surface was dL/dt. Therefore, dL/dt = 4.
I assumed d[itex]\theta[/itex]/dt = 4 m/s x 2[itex]\pi[/itex] rad/m = 8.
Therefore, I was able to calculate that dr/dt = 1/2.
I differentiated the cosine formula just to give myself a general idea of what I had to work with, but with two variable side lengths and an unknown [itex]\theta[/itex] I was at a loss.
Note: After quite a bit of searching, this was the closest value I found to help me out.
But in this example, a value for theta is given and two side lengths are known.
I think my main problem may be understanding the question. If someone could clarify it and give me some pointers that would be great!
Thanks!
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