Solve 2D Motion Homework: Wind Gust Accelerates Boat East

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A sailboat traveling east at 5.0 m/s experiences a gust of wind that accelerates it at 0.80 m/s² at an angle of 40 degrees north of east. To determine the boat's speed after 6 seconds, the acceleration must be broken down into its x (Ax) and y (Ay) components. The initial velocities are Vx0 = 5 m/s and Vy0 = 0 m/s, with the equations Vx = Vx0 + Axt and Vy = Vy0 + Ayt being used for calculations. The final speed is found by combining the components using the Pythagorean theorem, rather than simply adding them. The correct final speed of the boat is 9.21 m/s.
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Homework Statement


A sailboat is traveling east at 5.0m/s. A sudden gust of wind gives the boat an acceleration a =(0.80m/s^2) (40 north of east).



Homework Equations


What is the boat's speed 6\;s later when the gust subsides?

I know the answer is 9.21m/s, but I am having difficulty breaking down the acceleration into its components. How would you start this problem and do I need to find Ax and Ay or am i going about this the wrong way.



The Attempt at a Solution



So far I have
Vx0= 5m/s
Vy0= 0m/s
t=6s
Ax=?
Ay=?
and Think the equation I need to use is Vx= Vx0+Axt then do the same for Y
and combine the two .
 
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Okay I figure it out i was doing it right but when it cam e to combining the two components i was just adding them instead of finding the magnitude for velocity. Which involve taking the sqaure root of the squares of the components.
 
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