Consider an elevator that has a rated capacity of $\backslash (3,400\backslash$mathrm$\{$lb$\}\backslash ).$ It can transport people at the rate capacity between the first floor and the fifth floor, with a vertical distance of $16$ ft between each floor, in $5$ s $.$ Estimate the power requirement for such an elevator.

What is the work requirement for such an elevator $($in lbf $.$ ft $)?$

$\backslash [$

$\backslash$mathrm$\{$lbf$\}\backslash$cdot $\backslash$mathrm$\{$ft$\}$

$\backslash ]$

What is the power requirement in lbf $\backslash (\backslash$cdot $\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash )?$

$|$ lbf $\backslash (\backslash$cdot $\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash )$

How many lbf $\backslash (\backslash$cdot $\backslash )$ ft$/$s are equal to $1$ hp $?$

$\backslash [$

$\backslash$mathrm$\{$lbf$\}\backslash$cdot $\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}$

$\backslash ]$

Express the power requirement in hp$.$

hp