$(30$ pts$.)$ A tractor$-$trailer with a mass of $65,765lbm$ is climbing the hill on I$-40$W just past the

Crab Orchard rest area. At one position, the vehicle is at an elevation of $1,605$ feet above sea level

and has a speed of $60mph(88f\frac{t}{s}).$ Near the top of the hill, the vehicle is at an elevation of $1,795$

feet. Between these two positions, the tractor has provided $22,065$ Btu of work to increase the speed

of the vehicle. Determine the speed of the vehicle $(f\frac{t}{s})$ at the elevation of $1,795$ feet. Neglect

aerodynamic drag and rolling resistance.