A horizontal water jet with a flow rate of  and cross- sectional area of A drives a covere...

A horizontal water jet with a flow rate of  and cross- sectional area of A drives a covered cart of mass mc along a level and nearly frictionless path. The jet enters a hole at the rear of the cart and all water that enters the cart is retained, increasing the system mass. The relative velocity between the jet of constant velocity VJ and the cart of variable velocity V is VJ ‒ V. If the cart is initially empty and stationary when the jet action is initiated, develop a relation (integral form is acceptable) for cart velocity versus time.