Answer :
Let x be the distance of the fish to the fisherman and h be the height of the tip of fishing rod then we want to fiind dx/dt when x = 20. By property of similar triangle we have 12/x = h/20 --> h = 240/x
Differentiating w.r.t. we obtain dh/dt = (-240/x^2)*dx/dt --> dx/dt = [(x^2)/240]*dh/dt
At x = 20, dh/dt = 4 --> dx/dt = (-400/240)*4 = 20/3
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Differentiating w.r.t. we obtain dh/dt = (-240/x^2)*dx/dt --> dx/dt = [(x^2)/240]*dh/dt
At x = 20, dh/dt = 4 --> dx/dt = (-400/240)*4 = 20/3
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Answer:
v = 4.66 inch/s
Explanation:
As we know that the height of the rod and the distance from the fisherman is related to each other as
[tex]x^2 + y^2 = L^2[/tex]
now differentiate it with respect to time
[tex]2x\frac{dx}{dt} + 0 = 2L\frac{dL}{dt}[/tex]
here we know that
[tex]\frac{dL}{dt} = 4 inch/s[/tex]
now when
x = 20 ft and y = 12 ft then the length of the line is given as
[tex]L^2 = 12^2 + 20^2[/tex]
[tex]L = 23.3 ft[/tex]
now from above relation
[tex]\frac{dx}{dt} = \frac{L}{x}(\frac{dL}{dt})[/tex]
now we have
[tex]v_x = \frac{23.3}{20} (4 inch/s)[/tex]
[tex]v_x = 4.66 inch/s[/tex]
