A jogger runs around a circular track of radius 70 ft. Let (x,y) be her coordinates, where the origin is the center of the track

Question

A jogger runs around a circular track of radius 70 ft. Let (x,y) be her coordinates, where the origin is the center of the track. When the jogger's coordinates are (42, 56), her x-coordinate is changing at a rate of 19 ft/s. Find dy/dt.

dy/dt= ? ft/s

Answer 1

x^2 + y^2 = 4900

When x=42 and y=56, dx/dt = 19

implicit differentiation:

2 * x * dx/dt + 2* y * dy/dt = 0

x * dx/dt + y * dy/dt = 0

42 * 19 + 56 * dy/dt = 0

798 + 56 * dy/dt = 0

56 * dy/dt = -798

dy/dt = -14.25

the horizontal distance is decreasing at

a rate of 14.25 ft per second