In Problem 4.116, if \(M=100 \mathrm{~kg}, ho=999 \mathrm{~kg} / \mathrm{m}^{3}\), and \(A=0.01 \mathrm{~m}^{2}\), find the jet speed \(V\) required for the cart to be brought to rest after one second if the initial speed of the cart is \(U_{0}=5 \mathrm{~m} / \mathrm{s}\). For this condition, plot the speed \(U\) and position \(x\) of the cart as functions of time. What is the maximum value of \(x\), and how long does the cart take to return to its initial position?

Data From Problem 4.116

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4.116 A rectangular block of mass M, with vertical faces, rolls with- out resistance along a smooth horizontal plane as shown. The block travels initially at speed Uo. At t = 0 the block is struck by a liquid jet and its speed begins to slow. Obtain an algebraic expression for the acceleration of the block for t>0. Solve the equation to determine the time at which U = 0. Mass, M U P4.116, P4.117 V A