A duck has a mass of 3.0 kg. As the duck paddles, a force of 0.12 N acts on it in a direction due east. In addition, the current of the water exerts a force of 0.28 N in a direction of 47° south of east. When these forces begin to act, the velocity of the duck is 0.10 m/s in a direction due east. Find the magnitude and direction (relative to due east) of the displacement that the duck undergoes in 3.5 s while the forces are acting.
Magnitude _______ m
direction ________ degrees south of east
Magnitude _______ m
direction ________ degrees south of east
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East component of .28N. force = (cos 47) x .28, = 0.191N.
South component = (sin 47) x .28, = 0.205N.
Add east component to east velocity, = (.191 + .12) = .391m/sec.
Direction duck is moving = arctan (.205/.391) = 27.66 degrees, S of E.
Duck's velocity in the direction it is moving = 0.1/(cos 27.66), = 0.11278m/sec.
Displacement in 3.5s = 0.39473 metres.
South component = (sin 47) x .28, = 0.205N.
Add east component to east velocity, = (.191 + .12) = .391m/sec.
Direction duck is moving = arctan (.205/.391) = 27.66 degrees, S of E.
Duck's velocity in the direction it is moving = 0.1/(cos 27.66), = 0.11278m/sec.
Displacement in 3.5s = 0.39473 metres.