Final answer:
To determine the acceleration of the cart, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the force applied by the man pulling himself up the incline.
Step-by-step explanation:
Acceleration of the Cart
To determine the acceleration of the cart, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the force applied by the man pulling himself up the incline. Since the force applied is along the incline, we need to resolve it into its components: one parallel to the incline and one perpendicular to the incline. The perpendicular component doesn't contribute to the acceleration of the cart since it acts in the vertical direction. Therefore, we only need to consider the parallel component of the force. We can use the equation F_parallel = mass * acceleration to solve for acceleration. In this case, the mass is the combined mass of the man and cart, which is 100 kg, and the force parallel to the incline is ma. Plugging these values into the equation, we have 4215 N = 100 kg * acceleration. Rearranging the equation, we find that the acceleration is 42.15 m/s².