# Component Acceleration/Velocity

1. Oct 11, 2006

### mathewings

The problem is stated as follows:

A sailboat is travelling east at 4.10 m/s. A sudden gust of wind gives the boat an acceleration a=(0.500 m/s2,40.0° north of east). What is the boat's speed 5.90 s later when the gust subsides?

I've tried breaking it into component vectors, but no luck. Suggestions?

2. Oct 11, 2006

### radou

It's easier to write down the whole vectors. So, $$\vec{v}(t) = \vec{v}_{0}+\vec{a}\cdot t = 4.1 \vec{i} + (0.5\cos(40) \vec{i} + 0.5\sin(40) \vec{j})t$$. Plug in t = 5.9 and you'll have your velocity vector. (The speed is it's magnitude.)

3. Oct 11, 2006

### edavey8205

what are the equations you are using?

4. Oct 11, 2006

### mathewings

I totally understand your formula; I made the proper substitutions and it works. Thanks.

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