Q$3.(10$ points$)$ A $1200-m$ vertical curve connects a $-2\%$ grade to a $+3\%$ grade at station $145+00$ and elevation $84\mathrm{.}5m($VPI$).$

a$)$ Calculate the location and curve elevation of VPC$,$ VPI, VPT$,$ High$/$Low station and stations $141+00,143+00,147+00$ and $149+00.$ Sketch the curve and show stations.

b$)$ If the design speed is $80k\frac{m}{h},$ will this curve satisfy the minimum curve length $($hint: use Table $15\mathrm{.}4)$

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