A sailboat is heading directly north at a speed of 18 knots (1 knot = 0.514 m/s)

Question

A sailboat is heading directly north at a speed of 18 knots (1 knot = 0.514 m/s). The wind is blowing towards the east with a speed of 10.4 knots. (Both velocities are given relative to the Earth.) (a) Determine the magnitude and direction of the wind velocity as measured on the boat. what is the magnitude of the knots?. what is the direction north of east?. (b) What is the component of the wind velocity in the direction parallel to the motion of the boat (as measured on the boat)? what is the magnitude of the knots? what is the direction?

Explanation / Answer

Set up a right triangle: one side of the right angle is 20 units - the speed of the boat The other side of the right angle is 17 units - the wind speed Use pythagoras to find the hypotenuse which is the apparent wind speed seen by the sailboat, which will be from the northwest. For b) I assume they mean the component of the apparent wind velocity parallel to the direction of travel. Using the same triangle as before, its 20 kt: the headwind created by the boat's motion. (a). R = u - v R = 17{1,0} - 20{0,1} R = {17, -20} |R|² = 17² + (-20)² |R| = v689 = 26.2488 knots r = u • v r = 17{1,0} • 20{0,1} r = 0

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