a horizontal curve is to be designed for a section of a highway $($Rural area$)$ having a design speed of $80k\frac{m}{h}(50mph).$ Determine:

$3\mathrm{.}1.$ The radius of the curve if the super elevation is $4\%.(2$ marks$)$

$3\mathrm{.}2.$ The distance required to stop an average passenger car when brakes are applied on a $2\%$ downgrade if that vehicle was originally traveling at $50m\frac{i}{h}.(4$ marks$)$

$3\mathrm{.}3.$ The travelled distance before the driver initiates a physical response by changing direction to avoid collision. Vehicle's initial speed is $50mph.(2$ points$)$