can someone please help? I'm taking Calculus, but I'm really having trouble understanding the concept of related rates.
A jogger runs around a circular track of radius 55 ft. Let (x,y) be her coordinates, where the origin is the center of the track. When the jogger's coordinates are (33, 44), her x-coordinate is changing at a rate of 17 ft/s. Find dy/dt.
I tried making a triangle within the circle, and differentiating the Pythagorean Theorem to find the hypotenuse's length, but I'm stuck.
Thank you!
Best Answer
You did the right thing. It differentiates to:
$$2x\frac{dx}{dt} + 2y\frac{dy}{dt} =0$$
You know x, y, and $\frac{dx}{dt}$. Simply solve for $\frac{dy}{dt}$