A 20,000 kg rocket has a rocket motor that generates 3.0 x 10^5 N of thrust. Assume no air resistance. (a) What is the rocket's initial upward acceleration?

Video transcript

Hi, everyone. In this particular practice problem, we will have to calculate the spaceships vertical acceleration where we will have a 450 kg spaceship accelerating vertically upwards on the surface of Mars. And the amount of force produced by the spaceship engine is 2. times 10 to the power of four Newton. And we are asked to actually ignore the effect of resistant forces and we will have a gravitational acceleration on Mars at 3. m/s square. So in this particular practice problem, we will model the spaceship as a point like particle moving along the Y direction. We want to apply Newton's second law along the Y axis. And that is pretty much just saying F net at the Y direction will equals to M which is the mass of the spaceship multiplied by A Y just like. So, so the forces on the spaceship are the weight going downward and the force produced by the engine itself going upwards. So let's just imagine that this circle right here is our spaceship. So with this, we will have this force going upwards which is going to be the force by the engine F engine and we will have the force going downwards which is from the weight of the spaceship itself, which is W equals M times G just like so. Okay. So applying Newton's second law and we can determine that F net Y will equals to F engine minus M multiplied by G equals M multiplied by A Y. And we are being asked to calculate the spaceships for vertical acceleration, which is going to be A Y right here. So we can rearrange this so that A Y will equals to F engine minus M multiplied by G divided by M itself or the mess of the spaceship. So A Y can then be calculated because we know all these values right here. The F engine is going to be 2.5 times 10 to the power of four Newton. And then the mass of the spaceship is 4 50 kg. The acceleration, the gravitational acceleration is going to be the acceleration on Mars which is 3.72 m per second squared. And then divided of that is divided by the mass of the spaceship itself which is 4 50 kg. Therefore, A Y after plugging all these values will equals to 51.8 m per second squared. So we found that the spaceships vertical acceleration is going to equal to 51.8 m per second squared, which is going to equals to option C So option C where The spaceships, vertical acceleration of 51.8 m/s squared is going to be the answer to this particular practice problem. And I'll be all for this video. If you guys have any sort of confusion on this, please make sure to check out our other lessons, videos on similar topics on our website and that will be it. Thank you.