Question

astronaut's safety line is sabotaged while she is on a space walk, so she is no longer connected to the space shuttle. She checks and finds that her thruster pack has also been damaged and no longer works. She is 200 meters from the shuttle and moving with it. The is, she is not moving with respect to the shuttle. There she is drifting in space with only 4 minutes of air remaining. To get back to the shuttle, she decides to unstrap her 10-kg tool kit and throw it away with all her strength, so that it has a speed of 8 m/s. In the script, she survives, but is this correct? Her mass, including the space suit, is 80 kg.

Answer 1

To solve the astronaut's problem it is necessary to quickly consider the conservation of the moment.

By definition we know that,

Initial Momentum = Final Momentum

$m_1v_{1i}+m_2v_{i2} = m_1v_{1f}+m_2v_{if}$

Where,

$m_1 =$ Human mass

$m_2 =$ Tank mass

v is the initial and final velocity of each object

In the case of the initial part we know that it is in a state without movement with respect to the ship.

In the case of the final moment there is a speed injection thanks to the oxygen tank, then,

$m_1v_{1i}+m_2v_{i2} = m_1v_{1f}+m_2v_{if}$

$0 = m_1v_{1f}+m_2v_{2f}$

Re-arrange to find the final velocity for astronaut,

$v_{1f} = \frac{m_2v_{2f}}{m_1}$

Replacing

$v_{1f} = \frac{(10kg)(8m/s)}{80kg}$

$v_{1f} = 1m/s$

The astronaut has 4 minutes of air and must travel 200 meters therefore,

$v = \frac{x}{t}$

Re-arrange to find the time,

$t = \frac{x}{v}$

$t = \frac{200}{1}$

$t = 200s = 3min20s$

$3min20s<4min$

He/She will reach the spacecraft within the stipulated time