Example $5$

A car hits a tree at an estimated speed of $56k\frac{m}{h}$ on a $3\%$ downgrade. If the skid marks of $30$ meters observed on dry pavement $(f=0\mathrm{.}45),$ followed by $80$ meters $(f=0\mathrm{.}20)$ on a grass$-$stabilised shoulder, estimate the initial speed of the vehicle just before the pavement skid was begun. What are the factors you think might contribute to the stopping distance and how?