A two$-$lane, two$-$way road with a horizontal circular curve has the following design details.

Design speed $=65m\frac{i}{h}r$

The radius of the curve $=2,000ft$

Curve length $=820ft$

PC station $=14+10$

Cross slope $=2\%$

$e_{\text{m}\text{a}\text{x}}=10\%$

a$.$ Determine the super$-$elevation runoff $(L_r)$ for this curve. $(5$ Points$)$

b$.$ Determine the super$-$elevation tangent runout $(L_t)$ for this curve. $(5$ Points$)$

c$.$ Sketch this horizontal curve showing PC$,$ PT$,$ super$-$elevation runoff, and tangent runout points. $(5$ Points$)$