# Sailboat problem- components of acceleration

Sailboat problem-- components of acceleration

1. Homework Statement [/b]
A sailboat is travelling east at 5.70 m/s. A sudden gust of wind gives the boat an acceleration a=(0.800 m/s2,33.0° north of east). What is the boat's speed 5.50 s later when the gust subsides?
What is the boats new direction? as an angle (degrees north of east)

v(t)=v0+a*t

## The Attempt at a Solution

I divided the acceleration into its components, so ax= 0.8cos33 and ay= 0.8sin33 to give me the resultant acceleration to plug into the above formula. v(t)= 5.7 +(0.8cos33+0.8sin33)5.5 = 11.79 m/s, which is the wrong answer, but I'm not sure what I'm missing.
For the second question (what's its new direction), I used the y-component of the acceleration (0.8sin33) to find the the y component of velocity. So, vy=ay*t = 2.396 m/s.
I then used this to find the x and y position of the sailboat,
x= vx*t= 5.7 *5.5= 31.351 m east
y= vy*t= 2.396 * 5.5 = 13.18 north
I then used the tan-1 function to find the angle. So, tan-1 13.18/31.351 = 22.8 degrees north of east, which is also wrong.

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For the first part you can't simply add the velocitys because they are vectors. what to need to do is find the size of the resultant vector:

Vx=v(0)+v(x)*t Vy=v(y)*t

Use Pythagoras to get the size of the resultant:

V=(Vx^2+Vy^2)^1/2

For the second part you want the direction of travel so the angle you want is the angle of the resultant velocity:

arctan(Vy/Vx)

Got it, thanks!