A duck has a mass of 2.7 kg. As the duckpaddles, a force of 0.06 N acts on it in

Question

A duck has a mass of 2.7 kg. As the duckpaddles, a force of 0.06 N acts on it in adirection due east. In addition, the current of the water exerts aforce of 0.11 N in a direction of56° south of east. When these forcesbegin to act, the velocity of the duck is 0.11 m/s in a direction due east. Find the magnitudeand direction (relative to due east) of the displacement that theduck undergoes in 2.7 s while the forcesare acting. magnitude ______________ m direction ________° south of east magnitude ______________ m direction ________° south of east

Explanation / Answer

x be east, y be in north, we have: Fx = 0.06N+0.11N*cos(56) = 0.12N Fy = -0.11N*sin(56) = -0.09 N let ax be acceleration in x, and ay beacceleration in y, we have: ax = Fx /m = 0.12N/2.7kg =0.04m/s2 ay = Fy/m = -0.09N/2.7kg = -0.03m/s2 displacement in x and y are: Dx = 0.11*2.7s +(1/2)*0.04m/s2*(2.7s)2 = 0.44 m Dy =(1/2)*(-0.03m/s2)*(2.7s)2 = -0.11m D = [(0.44m)2 + (-0.11)2] =0.45m angle is , and = tan-1 (|0.11m|/.44m) = 14.040 answer: magnitude ______0.45________ m direction ______14.04__° south of east answer: magnitude ______0.45________ m direction ______14.04__° south of east magnitude ______0.45________ m direction ______14.04__° south of east

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