Objects with masses m$1=15\mathrm{.}0$ kg and m$2=8\mathrm{.}0$ kg are connected by a light string that passes over a frictionless pulley as in the figure below.

An illustration shows a rectangular block of mass m$1$ on the horizontal surface of a table. This is connected to another rectangular block of mass m$2$ by a cord that runs over a pulley placed diagonally at the corner of the horizontal surface of the table. The rectangular block of mass m$2$ is suspended vertically by the cord.

If$,$ when the system starts from rest, m$2$ falls $1\mathrm{.}00$ m in $1\mathrm{.}40$ s$,$ determine the coefficient of kinetic friction between m$1$ and the table.

$$k $=$