Any help with both these questions will be much appreciated. Thanks! The velocit

Question

Any help with both these questions will be much appreciated. Thanks!

The velocity of the wind relative to the water is crucial to sailboats. Suppose a sailboat is in an ocean current that has a velocity of 2.7 m/s in a direction 33 degree east of north relative to the Earth. It encounters a wind that has a velocity of 4.9 m/s in a direction of 48 degree south of west relative to the Earth. v_1 = 2.7 m/s v_2 = 4.9 m/s a_1 = 33 degree a_2 = 48 degree What is the magnitude of the velocity of the wind relative to the water m/s? What is the angle of the velocity of the wind relative to the water degrees S of W?

Explanation / Answer

let east be +x axis

a)

velocity of wind with resect water = velocity of wind with respect to ground - velocity of water with resoect to ground

= ( -4.9*cos(48) i - 4.9*sin(48) j) - (2.7*sin(33)i + 2.7*cos(33)j )

= (-4.75 i - 5.90 j) m/s

|v| = sqrt(4.75^2 + 5.9^2)

= 7.57 m/s <<<<<<<<<------------------Answer

b) direction:

theta = tan^-1(5.9/4.75)

= 51.2 degrees <<<<<<<<<------------------Answer

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