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A 68.5 -kg astronaut is doing a repair in space on the orbiting space station. She throws a $2.25-\mathrm{kg}$ tool away from her at 3.20 $\mathrm{m} / \mathrm{s}$ relative to the space station. With what speed and in what direction will she begin to move?

$0.105 \mathrm{m} / \mathrm{s}$

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{'transcript': "welcome to a new problem. This time we have an astronaut in space and they happened to have a mass mass of astronaut. So this is what's given well, given that the mosque often astronaut, is sixty eight point five kilograms and then we're also given that this is, you know, they're orbiting space. That's the astronaut, okay? And the mass happens to be sixty point five kilograms. And the aston what happens to throw Wei? Uh um a tool. You know, we don't know what the tool is, but the astronaut caused it The tool this way. Meaning that they're gonna have a push start because of Newton's stud law. So Newton start law, say's the action reaction forces the equal and opposite the mass off too, happens to be two point two five kilogram. And the tool is moving with the velocity that lost you. The two is three point two zero meters per second. We don't know what the velocity of the astronaut is, but that's not It is moving in the opposite direction. So that's what we're given. I want to find the, you know, find the velocity of the astronaut. Okay, So you're gonna use the law off conservation Oh, off momentum. Which says that the initial momentum off the system equals to the final momentum off the system. The initial momentum of the system. This happens to be the, um the tools. So we have the two. They're moving in opposite direction. So the tool, the mass ofthe two times the velocity off the two equals to the mask off the astronaut times the velocity off the asteroid on DH. So we want to solve it. Lost it. They asked or not that going to give us the aid? Because too MTV t over m A. We plug in the numbers the mass of the astronautical because sixty eight point five kilograms Um so sorry, dude. The to the tool the tool is two point two five kilograms of muscle. The tools to point two five program in the velocity of the two is three point two kilometres per second. Then divide that by the mass of the astronaut, which happens to be given a sixty eight point five kilograms that will give us a final velocity off the astronaut. That happens to be five. Plug in these numbers, they get two point two five times, three point two. Then you divide that by sixty eight point five kilograms in a super small number. And that makes sense because, you know, the Imagine a tool is trying to push the astronaut backwards. But, you know, it's in outer space, so still. Okay, Still some impact. Does your point one zero five two. Okay, five, one. Sorry. One, two, five, one. We gotta change this to one change. This one right here of this is one that Oh, you mean that this is one meters per second. Hope you enjoy the video. Uh, make sure you have a wonderful day. We wanted to find the velocity of the astronaut when they throw a tulip in outer space. Okay, Thanks. Bye."}

California State Polytechnic University, Pomona