How Does Force Affect a Duck's Displacement in Water?

[afcwestwarrior]

Homework Statement

A duck has a mass of 2.5 kg. As the duck paddles, a force of the water exerts a force of 20.0 N in a direction of 52 degrees south of east. When these forces begin to act, the velocity of the duck is .11 m/s in a direction due east. Find the magnitude and direction ( relative to due east) of the displacement that the duck undergoes 3.0 s while the forces are acting.

time=3.0s
angle=52 degrees
F=.20 N
F=.10N
Mass of duck=2.5 kg

Homework Equations

Acos 52 degrees
A sin 52 degrees

x=Vox(t) + Ax (t)^2/ 2

The Attempt at a Solution

I figured out the x component, and I got .20cos 52=.123 N
Then I added .10 N + .123 =.223 N
Then I figured out the acceleration .233 N/ 2.5 kg= .089 m/s^2
(if your getting a different answer then me it's because I rounded off, but I'm still using the exact numbers on my calculator such as
.1231222951)

Then I used that kinematic equation x= .11 m/s (3.0 s) + (.089 m/s^2) (3.0s)^2/2 = .7305 m

In the back of my book the answer is .78 meters. What did I do wrong.

 

[Doc Al]

Your solution is a bit hard to follow. Try solving for the x (east) and y (north) components separately. Find the components of the force, then the acceleration. Then solve for the displacement components, then the total displacement.

 

[afcwestwarrior]

Components of the force

 

[learningphysics]

Components of the force

The question mentions 20N. But you use 0.20N and 0.10N... I assume the 0.20 is a typo but where is the 0.10 coming from?