An 80-kg astronaut is stranded floating in space is 30 m away ...

Question

An 80-kg astronaut is stranded floating in space is 30 m away from his spaceship. He wants to return to his spaceship in 20 s. How fast must he throw his 2-kg space hammer, directly away from the spaceship, to accomplish this?

Accepted Answer

Hey guys got an interesting problem. Here's something that might seem like a sci fi movie or something like that. The idea here is we have an astronaut who stranded out in space. Let me go ahead and start drawing some some diagrams real quick. So we have this astronaut who's sort of stranded out in space like this and need to return back to his spaceship. So this gap here is a delta X, the distance of 30 m And Indians return in a time of seconds, otherwise he's going to run out of oxygen or something like that. The idea is we have to figure out how fast he's going to throw a space hammer so that's directly away from the spaceship in order to accomplish this. Why? So we have to throw the space ship the space hammer out this way because this is a push away problem if he throws the space hammer directly away from the spaceship, these two things are going to push off of each other and the recoil from that throw is going to send him back towards the spacecraft. Right? So I have this hammer here. That's a massive two. I've got the mass of the astronaut. I'm gonna call this and one which is 80 we want to find actually is we want to find what is V two final. So what happens is that things are initially together. Right. This is a push away problem and then finally they're gonna separate and we would need to figure out what's this V two final here. All right. So how do we do that? Well, this is really just a momentum conservation equation or momentum conservation problems. We're gonna go ahead and write our equation. So I'm gonna go ahead and write out my M1 V one initial plus M two V two initial equals and one V. One final plus M two V two final. So I've got my masses here. I'm just gonna write 80. So I'm gonna write 80 times something plus two times something equals 80 times something plus two times something. Right, right. The masses first. Basically what happens is if these two things are initially together right before they separate their initial velocity for both of the object is actually equal to zero. This is a push away problem. So zero goes in for both of these sides here. What about afterwards? What goes inside each one of these parentheses? Well, for the two kg space hammer, that's actually what we're looking for. V two finals. So this is my target variable. What goes inside here though? What's the final velocity for the astronauts? Well, I actually don't know what this is. So I'm gonna right now, I'm just going to call this V1 final here. All we know is that the aspirin has to return has to cover a distance of m in a time of 20 seconds. So even though we don't know what this speed is, we can actually calculate it because that's the clue that's being given to us in the problem. Otherwise we wouldn't be able to solve this because we have these two unknowns if you want to finally be to final. What the problem is actually telling us here is that using these two numbers using our 30 and 20 we can figure out that V one final in order for him to actually travel that 30 m in 20 seconds. He has to be going with the speed of 1.5 m per second. So, we know here is that the one final is going to be 1.5 towards the spaceship and it's going to be positive because it points in the right direction like this. All right. So we actually know what this number actually becomes. So on the left side we just get zero and on the right. So I'm going to get 80 times 1.5 and this is gonna be plus two times V two final. So when I got to multiply this out and then moving to the other side, you're gonna get negative 120 equals two times V two final. That's what we're looking for here. You just divide by two and you're gonna get a V two final of negative 60 m per second. Reason we got a negative number. That makes sense is because the space hammer has to go to the left, so it has to go the left, negative 60 m per second. It also has to be going very very fast because the mass of the space center is almost two and the astronaut needs enough momentum to have 1.5 m per second velocity this way, so he has to throw a space hammer, which is much lighter. He has to throw it much faster in order to get that speed. All right, so that's what this one guys let me know if you any questions.

An 80-kg astronaut is stranded floating in space is 30 m away from his spaceship. He wants to return to his spaceship in 20 s. How fast must he throw his 2-kg space hammer, directly away from the spaceship, to accomplish this?

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