A student has built a cart of massMwith an engine that can propel it with anon-constantforce. He launches the carton a horizontal surface from rest. Whilethe surface is horizontal, the cart'sengine provides a forceF(x)=cx2,proportional to the square of the distancextraveled, in the direction of the cart'smotion (cis some positive constant).Due to a design flaw, the engine stops working after the cart has traveled a distanceLas soon asthe cart encounters an incline that makes an angle with the horizontal. The cart continues upthe slope until it stops. Throughout the entire motion, a constant horizontal blowing force ofmagnitudeBis acting on the cart.Derive an expression for the vertical heightHthe cart has gained above the starting point when itcomes to rest, in terms of system parameters.