There is a vertical curve. The grade into the curve -3.6% and the grade out of the curve is 4.4%. If the design speed is 60 mph, calculate the minimum required length for the vertical curve based on stopping sight distance (Hint: Find the stopping sight distance for the design speed of 60 mph first and then use formula in the textbook to calculate minimum length for the vertical curve).

On solidification from a melt, the polymer polyethylene forms a semi-crystalline spherulite structure. (i) sketch an individual spherulite and label the amorphous and crystalline regions. (ii) draw a schematic to show the changes in specific volume with temperature during cooling from the melt, comparing it to the theoretical extremes of fully crystalline and fully amorphous (indicate tm and tg)