Answer:
dy/dt = -5/9 ft/s
Step-by-step explanation:
The track can be expressed as a circle or radius 45ft as follows:
[tex]x^{2} +y^{2} =45^{2} \\\\\\x^{2} +y^{2} =2025[/tex]
Implicit derivate for getting dy/dt
[tex]y^{2} =2025-x^{2} \\\\2y\frac{dy}{dt} =0-2x\frac{dx}{dt} \\\\[/tex]
Then:
[tex]\frac{dy}{dt} =\frac{-2x\frac{dx}{dt} }{2y} \\\\\frac{dy}{dt} =\frac{-x}{y} \frac{dx}{dt}[/tex]
Solving using the conditions. when x= 27 and y= 36 ; dx/dt=20 we have:
[tex]\frac{dy}{dt} =\frac{-27}{36}(20)=-15 ft/s[/tex]
