A $240$ lb painter stands $2\mathrm{.}00$ m from one end of a $6\mathrm{.}00$ m plank that is supported at each end by a ladder. How much of the painter's weight does the closest ladder to him support?

$($A$)160$ lb

$($B$)80$ lb

$($C$)240$ lb

$($D$)120$ lb