The deflection at the point of force application for the beam under loading shown below is given by $\displaystyle{y_p = - \frac{ Px^2 (L - x)^2 }{ 3EIL } }$ where $L$ is beam length, $P$ is load, $x$ is the position of the load. A load of $120 N$ is applied to a stell beam at a position $x = (4/7) L$. If the beam has a length of $2.2 m$ and a rectangular cross section $11.8 cm$ wide, determine its minimum beam height (in $mm$) such that deflection at $x$ does not exceed $0.0042 m$. Elastic modulus of steel is $200 GPa$. Report your result to three decimal places. Minimum beam height = $mm$