Discussion
The power (in kW) required to propel the boat is
Answer: B
The propulsive power is 20 kW.
Relative to the boat, water enters at the boat speed, 5 m/s, and leaves at 9 m/s. The thrust is the rate of change of its momentum:
\[ \begin{aligned} F &= \rho Q(V_{j} - V) = 1000(1)(9 - 5) = 4000\ \text{N} \\ P &= FV = 4000 \times 5 = 20000\ \text{W} = 20\ \text{kW} \end{aligned} \]
A common slip is to ignore the momentum the water already has relative to the boat when it enters, which inflates the thrust to 9000 N. Only the momentum difference times the boat speed gives the useful propulsive power, and 10, 50 and 90 kW do not follow from that balance.
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