Find the acceleration vector of the mass

[XwakeriderX]

Homework Statement

Two forces are acting on a 10.0 kg mass. The forces are:
F₁ = (12.3 x - 13.5 y) Newtons where x and y are unit vectors
F₂ = ( -6.30x + 11.9y) Newtons

A) Find the acceleration vector of the mass. Express your answer in unit vector
form.

Homework Equations

F=MA

The Attempt at a Solution

I added the two vectors getting
(6.0x-1.6y) Newtons then i divided it by the mass to get the acceleration

So my final answer is a= (0.6x-0.16y) m/s²

is this correct?

 

[Hotwir3]

So my final answer is a= (0.6x-0.16y) m/s²

is this correct?

You divided each vector (x and y) by ten, meaning that the result was that you were dividing it by ten, twice, resulting in 100.

Ex: if your vector was 20x + 20y, that magnitude is 400, so dividing each component by 10,
2x + 2y, you get a magnitude of 4.

You need to find the magnitude of 6x - 1.6y (Pythagorean) and divide THAT by ten, then use trigonometry to find the x,y components at that magnitude.
Or, a shortcut is to divide each component by sqrt(10) since the sqrt(10) ^ 2 is 10, so by dividing by the sqrt(10) twice (once to each component) you are ultimately dividing by 10.