Q$2-7$: A vertical curve is designed in a highway between an uphill slope $G_1=3\mathrm{.}0\%$ grade and a downhill slope $G_2=2\mathrm{.}0\%$ grade. If the design speed of this highway is $100k\frac{m}{h}r$ and the dangerous object and the driver's eye level are respectively at the $0\mathrm{.}26$ m and $1\mathrm{.}83$ m above the pavement surface. Determine the length of the vertical curve that will satisfy the sight distance requirement. $[10$ Marks$]$