A duck has a mass of 2.30 kg. As the duck paddles, a force of 0.110 N acts on it

Question

A duck has a mass of 2.30 kg. As the duck paddles, a force of 0.110 N acts on it in a direction due east. In addition, the current of the water exerts a force of 0.170 N in a direction of 49.0 ° south of east. When these forces begin to act, the velocity of the duck is 0.100 m/s in a direction due east. Find (a) the magnitude and (b) the direction (relative to due east) of the displacement that the duck undergoes in 3.10 s while the forces are acting. (Note that the angle will be negative in the south of east direction.)

I have not been able to reach the correct answer yet can someone please help me. I am not sure where I am going wrong.

Explanation / Answer

Fnet = 0.110i + 0.170cos49 - 0.170sin49 j N

Fnet = 0.222i - 0.128j    N

a = F / m = 0.222i - 0.128 j / 2.3   = 0.0965i - 0.0556 j   m/s2

s = ut + at2 /2

s = 0.1i X 3.1 + (0.0965i - 0.0556 j ) x 3.12 /2 = 0.774i - 0.267j m

a) magnitude |s| = 0.7742 + 0.2672   = 0.819 m

b) direction = tan-1 (0.267 / 0.774) = 19.03 degrees south of east.

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