A white whale of a physics problem

Classical Mechanics Level 5

There's a lot of forces involved in sailing - there's the thrust force provided by the wind, gravitational forces on the boat, drag forces from the water and air, etc. Balancing all these forces sometimes requires sailors to take precarious positions (as Hollywood has used to great effect.)

Consider a sailboat floating in the water at some instant in time. In x,y,z coordinates the bottom of the mast is located at the origin and the top of the mast is at (0,0,8) m, while the boat itself is oriented along the y-axis. The sail is approximately a triangle, and the three end points of the sail are near the bottom of the mast at (0,0,1), at the top of the mast at (0,0,8), and at (2.858,2.858,1). A gust of wind comes along, blowing towards the positive x-direction at a speed of 20 km/hr. The collision of the air molecules with the sail can be taken to be perfectly elastic.

What is the magnitude of the force in Newtons on the boat exerted by the gust of wind?

Details and assumptions

  • The density of air is \(1.2~kg/m^3\).
  • You may assume the boat is heavy enough that the gust does not make the boat move appreciably.

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