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**1. The problem statement, all variables and given/known data**

A boat is 400 kg and cruising along with a constant speed of 4.0 m/s in a direction 30 degrees north of east. The boat suddenly begins to feel a force from the wind that is 45 degrees north of east and has a magnitude of 100N. After a 10 second period what is the velocity vector of the boat?

**2. Relevant equations**

F = ma

v = v

_{o}+ at

**3. The attempt at a solution**

I'm wondering if I'm doing this right.

So I broke velocity into x and y components

v

_{xo}= 4cos30

v

_{yo}= 4sin30

Found the acceleration : f = ma

100 N = 400 kg * a

a = 1/4 m/s

^{2}

Broke acceleration into components

a

_{x}= 0.25cos45

a

_{y}= 0.25sin45

Plugged into equation v

_{f}= v

_{o}+ at

v

_{x}= 4cos30 + 0.25cos45 * 10

v

_{y}= 4sin30 + 0.25sin45 * 10

Then I would plug v

_{x}and v

_{y}into Pythagorean to find the magnitude of the velocity? and use inverse tan (v

_{y}/v

_{x}) to find the angle?