A vertical curve is needed to link two slopes, one with a gradient of $+6\mathrm{.}0\%$ and the other at $-5\mathrm{.}0\%.$

Given a design speed of $100k\frac{m}{h},$ calculate the curve length for the following scenarios:

When the driver needs to see the road markings.

When the driver needs to see an object $150$ mm in height.

Assume the driver's eye level is $2\mathrm{.}05$ meters above the road, the reaction time is $2\mathrm{.}5$ seconds, and

the longitudinal friction coefficient is $0\mathrm{.}18$ g $.$

Determine the required minimum stopping sight distance.

Check the sight distance criterion for the crest curve of case $1$ and case $2$