A driver traveling down a $4\%$ grade collides with a roadside object. The roadway has a posted

speed limit is $60$ mph $.$ The driver mentioned he strictly followed the speed limit$.$ The accident

investigation team indicates: braking skid marks started $300$ ft before the struck object.

a$.$ If the friction factor was measured as $0\mathrm{.}2,$ estimate the speed of the vehicle when it

struck the object.

b$.$ Estimate the minimum required friction factor so the $300$ ft skid marks can allow the

driver to safely stop before he would strike the object.