(II) A rocket with a mass of 2.45 x 10⁶ kg is launched by exer...

Question

(II) A rocket with a mass of 2.45 x 10⁶ kg is launched by exerting a vertical force of 3.55 x 10⁷ N on the gases it expels. Determine

(a) the acceleration of the rocket, Assume g remains constant, and ignore the mass of gas expelled (not realistic).

Accepted Answer

Welcome back. Everyone. In this problem. A missile with a mass of 2.65 multiplied by 10 to the 6 kg is launched vertically by applying a force of 3.45 multiplied by 10 to the seventh neons through gas expulsion, ignoring the mass of the expelled gasses and assuming constant gravitational acceleration. What is the missile's acceleration for our answer choices? A says it's 1.5 m per second. Cubed B 2.2 m per second squared, C 3.2 m per second squared and D 4.2 m per second cubed. No, let's try to draw a diagram to figure out what's going on here. So we're talking about a missile, a missile that has been launched vertically. So we know that it has that uh that like kind of like that fire behind it, I think. Ok, probably look something like that. Ok. And four arm missile oops for our missile based on the information given we know that the vertical force or the force that launches the missile is 3.45 multiplied by 10 to the seventh newtons. So let's call that force the thrust. Ok? And that force, the thrust is the upward force exerted by the missile and the gasses. Ok. And we also know that the missiles weight would be acting directly against the force since that force is vertical. So we have the missiles with which would have been MG where its mass is 2.65 multiplied by 10 to 6 kg. And we take the acceleration due to gravity G as 9.8 m per second squared. And from this information, we're trying to find the missiles acceleration. So let's call the missiles acceleration. A so how are we going to figure it out? Let's think about the information we have. Do we know anything that relates force the acceleration? Well, we can recall Newton's second law because recall that Newton's second law states that the sum of the forces is directly proportional to the acceleration by the formula, the sum of the forces equals mass multiplied by acceleration. Ok. So if we can find some of the forces and we can, and we already have the mass, then we can find the acceleration because no, based on this formula, this tells us that acceleration is going to be equal to the sum of the forces divided by the mass of the missile. Now, what do we know about the some of the forces that can help us? Well, the sum of the forces would be the net force. Ok? And in this case, the net force would be equal to the thrust minus the weight. So solving for a, OK, solving for our acceleration a in our formula, that means our acceleration is going to be equal to FT minus MG divided by M OK. Now we know what that force is. That thrust is because we know that our thrust is 3.45 multiplied by 10 to the seventh newtons. And we know that MG, we can substitute our mass which is 2.65 multiplied by 10 to the 6 kg. And we can multiply that by acceleration due to gravity which is 9.8 m per second squared. And all of that, all of that is being divided by our mass, which is 2.65 multiplied by 10 to the sixth kilograms. So that would be our acceleration. So to solve for acceleration, let's put this expression into our calculator. Now, when we do that, we should find that the acceleration is equal to 3.219 m per second squared. Recall that all of our answers were written to the nearest 10th of a meter per second squared. So we can rewrite our acceleration as approximately 3.2 m per second squared. So the miss as acceleration is approximately 3.2 m per second squared. If we look back on our choices, C is the correct answer. Thanks a lot for watching everyone. I hope this video helped

Struggling with Physics?

(II) A rocket with a mass of 2.45 x 10⁶ kg is launched by exerting a vertical force of 3.55 x 10⁷ N on the gases it expels. Determine
(a) the acceleration of the rocket, Assume g remains constant, and ignore the mass of gas expelled (not realistic).

Watch next

Vertical Forces & Acceleration practice set

Struggling with Physics?

(II) A rocket with a mass of 2.45 x 10⁶ kg is launched by exerting a vertical force of 3.55 x 10⁷ N on the gases it expels. Determine(a) the acceleration of the rocket, Assume g remains constant, and ignore the mass of gas expelled (not realistic).

Watch next

Vertical Forces & Acceleration practice set

(II) A rocket with a mass of 2.45 x 10⁶ kg is launched by exerting a vertical force of 3.55 x 10⁷ N on the gases it expels. Determine
(a) the acceleration of the rocket, Assume g remains constant, and ignore the mass of gas expelled (not realistic).