The girl at C stands near the edge of the pier and pulls in the rope horizontally at a constant speed of 6 ft/s . Determine how fast the boat approaches the pier at the instant the rope length AB is 50 ft.

Question

Accepted Answer

The length l of cord is
[latex]\sqrt{(8)^{2}+x_{B}^{2}}[/latex]+[latex]x_{C}[/latex]=l
Taking the time derivative:
[latex]\frac{1}{2}\left[(8)^{2}+x_{B}^{2}\right]^{-1 / 2}[/latex] [latex]2x_{B}\dot{x}_{B}[/latex]+[latex]\dot{x}_{C}[/latex]=0
[latex]\dot{x}_{C}[/latex]=6 ft/s
When A B=50 ft
[latex]x_{B}[/latex]=[latex]\sqrt{(50)^{2}-(8)^{2}}[/latex]=49.356 ft

[latex]\frac{1}{2}\left[(8)^{2}+(49.356)^{2}\right]^{-1 / 2} 2(49.356)\left(\dot{x}_{B}\right)[/latex]+6=0
[latex]\dot{x}_{B}[/latex]=-6.0783=6.08 ft/s [latex]\leftarrow[/latex]

Question : The girl at C stands near the edge of the pier and pulls in ...

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