A sailboat race course consists of four legs defined by the displacement vectors

Question

A sailboat race course consists of four legs defined by the displacement vectorsA,B,CandDshown above.

The values of the angles are ?1= 38.00, ?2= 37.00, and ?3= 23.00.

The magnitudes of the first three vectors are A = 3.3 km, B = 5.1 km and C = 4.6 km. The finish line of the course coincides with the starting line.

The coordinate system for this problem has positive x to the right, positive y as up and counter-clockwise to be a positive angle.

2) What is the value of ?4?

3) What is the value of Dy?

Explanation / Answer

A = 3.3( cos 38 i + sin38 j) = 2.72 i + 1.85 j B= 5.1( -cos 37 i + sin 37 j) = -4.26 i + 2.8 j C= 4.6( -cos 23 i - sin 23 j) = -4.3 i - 1.62 j distance of fourth leg = | A+B+C| = -5.84 i + 3.03j = 6.57 km. angle 4= 30.4 degrees Dy= 3.03 km.

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