An object whose mass is $300$ lb experiences changes in its kinetic and potential energies owing to the action of a resultant force R$.$ The work done on the object by the resultant force is $140$ Btu. There are no other interactions between the object and its surroundings. If the object's elevation change in $100$ ft and its final velocity is $200$ ft$/$s$,$ what is its initial velocity, in ft$/$s$?$ Let g $=32\mathrm{.}2$ ft$/$s$2.$