Question

An unfortunate astronaut loses his grip during a spacewalk and finds himself floating away from the space station, carrying only a rope and a bag of tools. First he tries to throw a rope to his fellow astronaut, but the rope is too short. In a last ditch effort, the astronaut throws his bag of tools in the direction of his motion, away from the space station. The astronaut has a mass of ma=102 kgma=102 kg and the bag of tools has a mass of mb=10.0 kg.mb=10.0 kg. If the astronaut is moving away from the space station at vi=2.10 m/svi=2.10 m/s initially, what is the minimum final speed vb,fvb,f of the bag of tools with respect to the space station that will keep the astronaut from drifting away forever?

Answer 1

The answer is "
`2.352 \ (m)/(s)`"

Step-by-step explanation:

`\to mass(m_1)=102 \ kg\\\\\to mass(m_2)=10 \ kg \\\\\to v=2.10\ (m)/(s)\\\\`

momentum before:

`\to p=(m_1+m_2)v`

`=(102+10)2.10\\\\=(102* 2.10 +10 * 2.10)\\\\=214.2+21\\\\=235.2`

momentum After:

`\to p=(m_1+m_2)v`

`=(102* 0 +10 * v)\\\\ =(0 +10v)\\\\=10v\\`

Calculating the conservation of momentum:

`\to \text{momentum before = momentum After}`

`\to 235.2=10v\\\\\to v= (235.2)/(10)\\\\ \to v=2.352 \ (m)/(s)`