A duck has a mass of 3.0 kg. As the duck paddles, a force of 0.12 N acts on it i

Question

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 0.19 N in a direction of 57° south of east. When these forces begin to act, the velocity of the duck is 0.09 m/s in a direction due east. Find the magnitude and direction (relative to due east) of the displacement that the duck undergoes in 3.6 s while the forces are acting.

I have found my magnitude to be 0.87m, but am having trouble figuring out the direction.

Explanation / Answer

East component of .19N. force = (cos 57) x .19, = 0.103N.
South component = (sin 57) x .19, = 0.159N.
Add east component to east velocity, = (.103 + .12) = .223m/sec.

Direction duck is moving = arctan (.159/.223) = 35.489 degrees, S of E.

Duck's velocity in the direction it is moving = 0.09/(cos 35.48), = 0.1105m/sec.
Displacement in 3.6s = 0.3979 metres.

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