Hey, guys. Let's check this one out. So you've got this 2 kilogram box. Right? So this 2 kilogram box like this, we're on a rooftop or something like this. We're basically going to drop it straight down. So there's basically just going to be some weight force once you drop it. However, there's also going to be a horizontal wind force that pushes this thing horizontally like this. We know this wind force is going to be 3 newtons, and we want to figure out the direction of the box's acceleration. So, I've got one force that acts horizontally, another one acts vertically, and I want to figure out what is the acceleration of this box.
Well, basically, if you think about it, these 2 forces, one to the right and one down, are going to produce an acceleration that acts this way, like this, and I want to figure out what is the direction of this theta here or what is the direction of this a. Alright. So, what I want to do is first, I want to draw the free body diagram. I've got this like this. I've got my weight force, this is my mg. If I go ahead and figure that out, this is 2 times 9.8, and this is actually going to be 19.6. We also have our wind force, our Fw, which is to the right, and that's 3 newtons. And that's basically it. Right? There's no tensions. And because this thing is traveling in the air, there's no normal force or friction.
The next thing I would have to do is I would want to decompose all my 2-dimensional forces, but I actually don't have any, so I can just skip that step. What I want to do is I want to write F = ma in the x and y axis. So, if you want to figure out the acceleration here, the direction of this acceleration, this is theta a, then the way I would do this is by getting the tangent inverse of the y components over the x components. So in order to do this, and to get ay and ax, I'm going to have write F = ma in both x and y axis. Right? So, on my x axis, I've got F = max, and in the y axis, I'll have F = may.
So now on the x axis, the only force that I have is Fw. So, this is Fw = m ax. Really, this is just 3 newtons equals 2 times ax. So ax is equal to 1.5 meters per second squared. And that's one part of the puzzle. Now, I just need to figure out what ay is equal to. So, remember that this thing is going to be pushed in the horizontal and the vertical so you can assume that the acceleration is 0 on either axis. What are my only forces that are acting in the y axis? I basically just have my negative mg. And that's just because I'm going to use the convention that up and to the right is positive, as I usually do.
So, I've got negative mg equals m ay. You'll see that the m's cancel and basically your ay is equal to negative g, which is just negative 9.8 meters per second squared. This makes sense because if the only downward force that's acting on this object is the weight force, then you're just going to accelerate at 9.8. That's what everything does. Right? So, basically, I've got those two numbers. So, whoops. Then I've got my negative 9.8 and now I can just go ahead and solve for theta a. So theta a is just going to be tangent inverse. Now I've got my ay component, which is negative 9.8, divided by my x component, which is 1.5. And if you go ahead and work this out, you're going to get negative 81 degrees. This negative just means that it's below the horizontal, and that's what we should expect because it points downwards like this. So that's our answer, 81 degrees below the horizontal. Let me know if you guys have any questions.