Answer:
11.25 ft/sec
Step-by-step explanation:
Given that 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.
Then we know x,y satisfies the equation of the circle as
[tex]x^2+y^2 = 55^2[/tex]
Let us differentiate this implicit function with respect to t
[tex]2x \frac{dx}{dt} +2y \frac{dy}{dt} =0[/tex]
At this point, dx/dt 15 and x=33. y =44
Substitute to have
[tex]2(33)(15) +2(44) \frac{dy}{dt}\\=0\\\frac{dy}{dt}=11.25[/tex]
dy/dt = 11.25 ft /s
