(Solved): 3. A horizontal water jet with a flow rate of V and cross-sectional area of A drives a covered ca ...

3. A horizontal water jet with a flow rate of $\stackrel{?}{V}$ and cross-sectional area of $A$ drives a covered cart of mass $m_c$ 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 water jet has a constant velocity of $V_J$ and the cart moves at a constant velocity equal to half of the jet, $V=V_J/2$. If the cart is initially empty when the jet action is initiated, develop a relation (integral form is acceptable) for the reaction force acting on the cart in the horizontal direction.