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Q4. (a) The force, F, produced on a ship’s rudder is proportional to the area, A, of the rudder, the square of the ship’s speed, V, in knots and the sine ratio of the rudder angle, α.

For a ship travelling at 10 knots, with a rudder area of 24 m² operating at an angle of 23°, the rudder force is 144 kN.

Calculate the force on a similar rudder of area 29 m2 operating at an angle of 15° when the ship’s speed is 14 knots. (8)

(b) Y = (3 + 9/(x - 2))/(x – 3/(x - 2))

Express as a single algebraic fraction in its simplest form. Y (8)