homework and exercises - How do I find the horizontal acceleration of a body given its mass and the force that acts on it?

My issue

I have the mass of a body and the force that is acted on a body. I am trying to calculate the horizontal acceleration and to understand how the horizontal acceleration is connected with the angle $\alpha$ that the direction of the force makes with the horizontal.

What I tried

Let's write down formula of Newton's Second Law:

$$F= ma$$

I can easily calculate the acceleration by properly inverting the formula: $$a = \frac{F}{m}$$

However, I shouldn't forget the force forms an angle $\alpha$ with the x-axis. Hence I should consider the acceleration using $cos(\alpha^\circ)$.

My question

What am I missing? In which way is the horizontal acceleration connected by the angle $\alpha$ the force forms?

Answer

Your $2.0 \frac{m}{s^2}$ is the acceleration in the direction of the force, at $60°$ angle with the x-axis. You need to find the component of the acceleration in the direction of the x-axis. If your acceleration is completely in the y-direction, your object will have $0$ acceleration in x-direction. If it is completely in the x-direction, it will have those $2.0 \frac{m}{s^2}$. Now, your scaling factor will be $1$ if the angle is $0°$ and $0$ when it is $90°$. The cosine does just that: $$a_x = \frac{F}{m} \cos(60°)$$