Ropes for mountain climbing are designed to stretch a little bit, so that if a person falls the rope won't cause injury by slowing them down too quickly. When Matt hangs from a $25$ m long climbing rope, it stretches about $1\mathrm{.}8$ m$.$ Matt has a mass of $42\mathrm{.}6$ kg$.$ Calculate the rope's force constant. Use g $=9\mathrm{.}8$ m$/$s$2.$