Calc I Related Rates Question involving a Circle Two runners at the same point begin running in opposite directions along a
circular track of radius $100$m at a speed of $5$m/s. At what rate is the (shortest)
distance between them growing after $10$s?
i have done many related rates problems but none like this and have no idea where to even start any help would be appreciated!
 A: Actually I've answered this question before and I cannot comment because I'm new user hers
but Here's the answer
Let's assume they travel with constant velocity $v$, and Radius of circle be $r$
After time $t$ Arc length will be $vt$ 
$$l=vt=r\theta$$
and angle subtending that arc will be 
$$\theta=\frac{vt}{r}$$ now shortest distance between them will be $$x=2r\sin\theta$$
Now we have our relation
$$x=2r\sin\left(\frac{vt}{r}\right)$$
Now rate of change of shortest distance between them is
$$\frac{dx}{dt}=2r\frac{v}{r}\cos\left(\frac{vt}{r}\right)=2v\cos\left(\frac{vt}{r}\right)$$
Now plug in values
Here's a rough diagram if it helps

Note:
In figure after time $t$ their respective positions are shown by $A$ and $A'$
$$x=AA'$$
$$r=BA=BA'$$
$$\angle ABO=\angle A'BO=\theta$$
A: Hint: Find $\frac{d\theta}{dt}$, and $\theta$ at 10 seconds. Then, you can find a equation involving the distance, since you know the radius, and the angle $\theta$ between them, and thus can write a formula for the distance. Take the derivative with respect to $t$, and you should get your answer.
