Problem $1$: $50$ pts A rear$-$wheel$-$drive electric car is traveling uphill at a speed of $25$ mi$/$h on a slope covered with hard$-$packed snow, with a grade of $4\mathrm{.}5\%.$ The car has an aerodynamic drag coefficient $=0\mathrm{.}30,$ a frontal area $=222,$ and a weight $=2800$ lb$.$ The wheelbase is $120$ inches, and the center of gravity is located $24$ inches above the ground and $50$ inches behind the front axle. The air density is $0\mathrm{.}002378$slugs$/$ft$3.$ The cars electric motor generates $100$ ft$-$lb of torque, and the overall gear reduction ratio is $3\mathrm{.}8.$ The wheel radius is $14$ inches, and the mechanical efficiency of the drivetrain is $88\%.$ If there is a traffic light $210$ meters ahead of the car, and the light is turning yellow in $12$ seconds, keeping yellow for $2$ seconds, and then turning red. Will the car pass the traffic light successfully?