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Calculating the maximum velocity of a jet ski

The ski boat's jet propulsive system draws water in at point A (at the middle of the bottom of the boat) and expels it at B (at back of boat) at 80ft/s relative to the boat. Assume that the water drawn in enters with no horizontal velocity relative to the surrounding water. The maximum mass flow rate of water through the engine is 2.5 slugs/s. Hydrodynamic drag exerts a force on the boat of magnitude 1.5v lb, where v is the boat's velocity in feet per second. Neglecting aerodynamic drag, what is the ski boat's maximum velocity?

Solution Preview

Forces on the boat:

There is a propulsive force generated by the engine, which by speeding up the water flowing about it, generates a force due to changes in momentum (Newton's 2nd Law states that a force is generated by changes in momentum and vice versa).

There is also a drag force which opposes the motion created by the engine, and this is proportional to the ...

Solution Summary

This solution provides an explanation regarding maximum velocity, taking into account propulsive force and drag force and using equations to find the final velocity solution.