A small rocket burns 0.0500 kg of fuel per second, ejecting it as a gas with a velocity relative to the rocket of magnitude 1600 m/s. (a) What is the thrust of the rocket?

Video transcript

Everyone in this problem. We have a rocket. Okay, it's using 200 kg of fuel per hour. The burn fuel is ejected from the exhaust with a velocity of 2500 km an hour relative to the rocket. Okay? We're asked to find the thrust of the rocket. Alright, So to find the thrust. Okay, So let's consider F. T. The force of the thrust. Well, this is going to be V. X E X. Okay, so the exhaust velocity times delta M over delta T. All right, well, let's think about all of these values. Okay, so this the rest is what we're trying to find. Let's try to figure out if we have everything we need for this equation. We think about the exhaust velocity. Well, here we have an exhaust velocity of 2500 km an hour. Okay? And fuel is being ejected so we're losing that fuel. Okay. And so that's going to be negative kilometers per hour. Okay, And just be careful here. Some textbooks and some professors use different conventions so some people will put the negative directly in this formula and then call this exhaust velocity positive. Okay, it works out the same. It's just which convention the textbook or the professor is using. Okay, so just double check before you do problems like this, on what convention you should be using. Okay, Alright, so we have 2500 kilometers an hour. Let's put this into our standard units of meters per second. So this is going to be negative 2500. We're gonna multiply by a and we're going to divide by 60 minutes and 60 seconds. And this is going to give us meters per second. And this gives us a exhaust velocity of -694. m/s. Okay. All right. So, we have this exhaust velocity now we need this delta M over delta T. And that's the change in mass Over the change in time. We're told That the rocket uses 200 kg of fuel per hour. Okay, so the change in mass over the change in time is going to be -200 kg per hour while converting this into seconds. This is gonna be 200 sorry, negative 200 kg divided by 60 minutes, 60 seconds, um per second. Alright, which gives a Delta M over density negative 0.055 repeated kg per second. Alright, So, we have our exhaust velocity. We have our delta M over delta T. All of our units have been converted into our standard units so we can find the thrust. So F. T. It's going to equal to minus 694.44 m per second Times negative 0.055 repeated kilograms per second. Let me just wine here. All right. And this is going to give us a final thrust of 38. kg meter per second squared. Okay? And recall that this is just equal to the unit of newton. Okay, So we got 38.6 newtons for our thrust force and that's going to correspond with answer C. That's it for this one. Thanks everyone for watching. See you in the next video.