It's where you go from to You've missed a cancellation by 2.
A runner sprints around a circular track of radius 100 m at a constant speed of 7 m/s. The runner's friend is standing at a distance 200 m from the center of the track. How fast is the distance between the friends changing when the distance between them is 200 m.
I attached a sketch of the problem so you can visualize what I'm doing.
I decided to use the law of cosines, is the distance between them:
Differentiating with respect to
When the
So no I plug everything into the equation for the time derivative of s:
This is very close to the answer in my book which is
I can't seem to find where I want wrong.