Alright, guys. Let's check out this next one here. We have a 1,000 kilogram rocket that is accelerating upwards due to some thrust. So I've got this rocket like this. I know the mass is 1,000, and I got a couple of forces on it. During the first 20 seconds of its motion, we know the weight force or the force of gravity downwards, this is my w, is going to equal 10,000. We also have a couple of other forces like the force of thrust. That's basically like an applied force. So what I'm gonna do is I'm gonna call this ft for thrust. I also have a force of air resistance that's acting downwards because this rocket is gonna start accelerating. We're gonna start moving upwards like this. So what happens is the air resistance, I'm gonna call this fair, is going to point downwards, and I know this is 5,000. I also know this thrust is 25,000. Alright? So I've got all these forces. There's no normals or frictions or anything like that. What I wanna do is figure out the rocket's velocity after 20 seconds. We know that the initial velocity is going to be 0 because it's going to start from rest, but then later on, it's going to have some final velocity. So this final velocity is actually what I'm looking for here. So if I wanna figure out vfinal, I'm gonna have to list out all of my other kinematics variables, right, like my initial velocity. I also want the Δy, and then I have the acceleration and time. So I'll need all of these things. The Δy, I don't know what that is. I know that v0 is 0, starts from rest. The acceleration, I don't know either and I also, I know the time is 20 seconds. Right? So this is going to be my 20 seconds here. So we have here that the 2 out of 5 variables. Right? We have 2 out of 5, which means we can't actually use an equation to solve for vfinal yet. We're gonna need another one of our variables. Just like we have done before, when we get stuck, we're gonna try to use this, we're gonna try to figure out this a by using f=ma. So we're gonna use f=ma to figure out acceleration and we're now just gonna add all of our forces in the vertical direction. Right? All of our forces act only along the y-axis. So what happens is this rocket is traveling upwards, so I'm just gonna choose the upwards direction to be positive. And so that means that our ft is positive when we expand out our Σf. fair is going to be downward so it gets a negative. And then our weight force is also going to be negative as well. So this equals mass times acceleration. Remember, I wanna figure out this a here so I can plug it back into this, into my kinematics variables and then pick an equation. Alright? So now I just replace all the values that I know. This is 25,000 Then I've got this fair is 5,000, and then I've got minus this 10,000 from the weight. And this equals mass which is 1,000 times acceleration. Alright, so if you work all this out what you're gonna get is 10,000. So you're gonna get 10,000 over here is equal to 1,000 times a. So that just means that our acceleration is 10 meters per second squared. Alright? So our acceleration is 10, which means we can now have enough information to figure out a kinematics equation, right? So we now we have 3 out of 5, and now we're gonna go ahead and just pick out one of your equations. So I'm gonna go over here. If I wanna find out the final velocity, the final velocity is basically going to be the equation that ignores my delta x. Right? So I'm gonna ignore my Δy over here, and that's just gonna be equation number 1. So I've got equation number 1, which is vfinal equals vinitial plus at so if we want vfinal this is just gonna be 0 plus now I've got an acceleration of 10 and then I've got in a time of 20. So this is basically just gonna be 200 meters per second. Alright? So look through your answer choices and it's answer choice a. That's it for this one, guys.
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