F eworkS Begin Date: T22018 1200:00 AM-Due Date: T2ZOIS TT59.00 PM End Date: 212
ID: 1579005 • Letter: F
Question
F eworkS Begin Date: T22018 1200:00 AM-Due Date: T2ZOIS TT59.00 PM End Date: 2122O1 13900 896) Problem ll: The velocity of the wind relative to the water is crucial to sailboats. Suppose a sailboat is in an ocean current hat has a velocity of 2.3 m/s in a direction 34° east of north relative to the Earth. It encounters a wind that has a velocity of 44 m/s n a direction of 55° south of west relative to the Earth. 50% Part (a) What is the magnitude of the velocity of the wind relative to the water, in meters per second? Grade Summary Deductions 096 Potential 100 sino coso tan7 s9 cotanasin acos0 atanO acotan sinh s tanh cotanhO Submissions 4 5 6 12 3 per attempt) etailed view Degrees O Radians Submit 1 give up Feedback: deduction per feedback. Hints: deduction per hint Hints remaining: - 50% Part (b) What ia the angle of the velocity of the witnd relative to the water degrees south of west?Explanation / Answer
the problem can be solved vectorially
a)velocity of ocean current in vector form = 2.3sin34 i + 2.3cos34j = 1.286i+1.907j m/s
velocity of wind in vector form = -4.4cos55i-4.4sin55j=-2.524i-3.604j m/s
velocity of wind relative to water = -2.524i-3.604j-(1.286i+1.907j) = -3.81i-5.511j m/s
magnitude of velocity = sqrt(3.812+5.5112)=6.7 m/s
b)Angle of velocity of the wind relative to water degrees South of West = tan-1(5.511/3.81)=55.34o
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