## Question:

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.

## Step-by-step

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

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