ENGR $220$: Statics

Problem #$2(12$ points$)$

The man pushes the $100-lb$ crate along the floor with a constant speed. The crate suddenly reaches a rough patch for which ${}_k=0\mathrm{.}4$ and ${}_s=0\mathrm{.}48.$ If the man continues to push with just enough force to keep the crate sliding, what is the largest height off the floor, $h,$ at which the man can apply force P with out causing the crate to tip as it slides over this rougher surface?