A freshwater jet boat takes in water through side vents and ejects it through a nozzle of diameter \(D=75 \mathrm{~mm}\); the jet speed is \(V_{j}\). The drag on the boat is given by \(F_{\text {drag }}=k V^{2}\), where \(V\) is the boat speed. Find an expression for the steady speed, \(V\), in terms of water density \(ho\), flow rate through the system of \(Q\), constant \(k\), and jet speed \(V_{j}\). A jet speed \(V_{j}=15 \mathrm{~m} / \mathrm{s}\) produces a boat speed of \(V=10 \mathrm{~m} / \mathrm{s}\).

(a) Under these conditions, what is the new flow rate \(Q\) ?

(b) Find the value of the constant \(k\).

(c) What speed \(V\) will be produced if the jet speed is increased to \(V_{j}=25 \mathrm{~m} / \mathrm{s}\) ?

(d) What will be the new flow rate?