Question $8(15$ points$)$: A car is traveling at $40$ mph in the country at night on a wet road through a $120$ ft $.$ long sag vertical curve. The entering grade is $-3$ percent and the exiting grade is $4\mathrm{.}0$ percent. A tree has fallen across the road at approximately the PVT$.$ Assuming the driver cannot see the tree until it is lit by her headlights, is it reasonable to expect the driver to be able to stop before hitting the tree?