Relating force, displacement, time and velocity

[Ohoneo]

Homework Statement

A duck has a mass of 2.7 kg. As the duck paddles, a force of 0.13 N acts on it in a direction due east. In addition, the current of the water exerts a force of 0.20 N in a direction of 54° south of east. When these forces begin to act, the velocity of the duck is 0.13 m/s in a direction due east. Find the magnitude and direction (relative to due east) of the displacement that the duck undergoes in 2.3 s while the forces are acting.

Homework Equations

F = ma
v²-v₀² = 2a(x-x₀)
x = x₀+v₀t+1/2 at²
v = vat

The Attempt at a Solution

First, I drew a diagram. The .13 N is a vector going from right to left. Then, the .20 N vector connects and heads south east. Because it is 54 degrees south of east, that means the interior angle where the two vectors join is 126 degrees.
I then found the results.
I found the resultant vector to be .293 N.
I then used the F=ma equation to find acceleration which I found to be .1096 m/s₂.
I then plugged this into v = v a t (v = .13 + .1096 (2.3)) to find that final velocity was .38 m/s.
I then plugged all of this into the equation v²-v₀² = 2a(x-x₀).
I substituted: .38²-.17² = 2(.1096)x
I solved for x to be .589
I then used my diagram to find tan^-1(.2/.13) to get 59 degrees as an answer.

Unfortunately, all of this was wrong.

 

[Sniperman724]

try splitting up the .2oN force in a direction of 54 degrees south of east into vectors, and use those numbers to solve the rest.

 

[Ohoneo]

try splitting up the .2oN force in a direction of 54 degrees south of east into vectors, and use those numbers to solve the rest.

Oops, sorry. I should have clarified that I did that. That's how I got the resultant vector; I found the components of the vector that had a force of .20 N. The vector in the x direction was .12 N and the vector in the y direction was -.16 N.

 

[verty]

As the duck paddles, a force of 0.13 N acts on it in a direction due east.
...
First, I drew a diagram. The .13 N is a vector going from right to left.

Right to left is due west.

 

[Ohoneo]

Right to left is due west.

Okay, apparently I'm terrible at explaining myself. I drew it left to right. Regardless, I made east the positive direction and south is the negative direction.