Finding the direction of acceleration in degrees

[kathyt.25]

Homework Statement

"Forces of 10.6 N north, 19.1 N east, and 16.0 N south are simultaneously applied to a 3.62 kg mass as it rests on an air table. What's the direction of acceleration in degrees (Take east to be 0 degrees and counterclockwise to be positive.) "

Using components, I already figured out the magnitude of acceleration.
a=5.48m/s/s
Fnet=19.8N --> broken into components: F(x)=19.1N, F(y)=-5.4N

Homework Equations

Fnet=ma
Trig ratios for sin and cos

The Attempt at a Solution

Using components, I figured out the total force in the x and y directions, and then used the pythagorean theorem to calculate the Fnet.

To find acceleration, I then isolated for a = Fnet/m = 5.48m/s/s

However, I'm having a lot of trouble figuring out the direction of the acceleration, and I don't know why! It's simple trig ratios.

cos(thetha) = F(x)/Fnet = 19.1/19.8
(theta) = 15.3 degrees
Its positive because the counterclockwise direction is positive.

Am I doing it wrong because they are asking for the direction of acceleration, and I'm using the direction of Fnet? I don't see how I can use acceleration in the trig ratios though, since acceleration is only in the direction of Fnet... not the components on the x and y axis.

 

[Dick]

You don't need Fnet to find the angle. Use tan(theta)=F(y)/F(x). Using the rounded value of Fnet gives you a fairly large error in this case. The direction of the acceleration is the same as that of the force. So you have the angle relative to the x (east-west) axis. Now look at the force vector. Is that 15 degrees clockwise or counterclockwise from east?