$($d$)$ Figure $5$ shows a $1964$ Amphicar Model $770$ amphibious car reproduced from a CTV News Ottawa article "Amphicar makes waves on the Rideau River". The car has a mass of $1050$ kg $,$ a $43$ hp rear$-$mounted engine, rear$-$wheel drive, a four$-$speed manual transmission, and twin propellers for propulsion while afloat. It is capable of achieving a top speed on land of $110k\frac{m}{h}$ and a top speed in the water of $7$ knots $(13k\frac{m}{h}).$ In its lowest gear with peak engine torque $(88\mathrm{.}1$ Nm $)$ it is capable of delivering $3566$ N of tractive force to the rear wheels.

Figure $5$: Amphicar Model $770.$

Assuming a coefficient of road adhesion of $0\mathrm{.}4$ corresponding to a wet and slippery boat ramp, a coefficient of rolling resistance of $0\mathrm{.}02,$ vertical load on the driven wheels of $5665$ N $,$ and negligible aerodynamic drag at low speed, determine the steepest ramp that the car could drive up at constant speed in its lowest gear when leaving the water.