Problem $15\mathrm{.}27$

The winch delivers a horizontal towing force $\backslash (\backslash$mathbf$\{$F$\}\backslash )$ to its cable at $\backslash ($ A $\backslash )$ which varies as shown in the graph. $($Figure $1)$

Part A

Determine the speed of the $60$ kg bucket when $\backslash ($ t$=23\backslash$mathrm$\{$~s$\}\backslash ).$ Originally the bucket is moving upward at $\backslash ($ v$\_\{1\}=3\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$

Express your answer with the appropriate units.

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