Question

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 15 ft/s. Find dy/dt.

Answer 1

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

$x^2+y^2 = 55^2$

Let us differentiate this implicit function with respect to t

$2x \frac{dx}{dt} +2y \frac{dy}{dt} =0$

At this point, dx/dt 15 and x=33. y =44

Substitute to have

$2(33)(15) +2(44) \frac{dy}{dt}\\=0\\\frac{dy}{dt}=11.25$

dy/dt = 11.25 ft /s