$10.)(25$ Points$)$ The motor$/$winch assembly shown in the following figure exerts a tension of $\backslash ($ T$=\backslash$left$(600+2$ s$^\{2\}\backslash$right$)\backslash )($in "Newtons" when $"$s$"$ is in meters$)$ on the "Top" cable shown below. If the crate has a mass of $100$ kg and is initially at rest on the ground, Determine,

i$.)$ The speed of the crate the instant it has risen to a height of $\backslash (\backslash$mathrm$\{$s$\}=15\backslash$mathrm$\{$~m$\}\backslash ).$

ii$.)$ The power output from the motor$/$winch assembly $($expressed in units of hp$)$ the instant the crate has been lifted to a height of $\backslash (\backslash$mathrm$\{$s$\}=15\backslash$mathrm$\{$~m$\}\backslash )$ above the ground.

iii.$)$ The electrical power supplied to the motor $($expressed in units of KW$)$ the instant the crate has been lifted to a height of $\backslash (\backslash$mathrm$\{$s$\}=\backslash$frac$\{19\}\{15\backslash$mathrm$\{$f$\}\}\backslash )$ above the ground if the motor has an efficiency of $\backslash (\backslash$epsilon$=0\mathrm{.}80\backslash ).$