An astronaut in her space suit has a total mass of 87.0kg including suit and oxygen tank. Her tether line loses its attachment to her spacecraft while she's on a spacewalk. Initially at rest with respect to her spacecraft, she throws her 12.0kg oxygen tank away from her spacecraft with a speed of 8.00 m/s to propel herself back toward it. (a) determine the maximum distance she can be from the craft and still return withn 2.00 min( the amount of time the air in her helmet remains breathable). (b) Explain in terms of Newton's laws of motion why this strategy works.

when she throws the tank away from spacecraft , she will have a velocity in opposite direction ie towards the spacecraft . This happens due to conservation of momentum . She creates a momentum away so that she can get a momentum towards the spaceship.

So

m₁ v₁ = m₂v₂

12 x 8 = ( 87 - 12 ) x v₂

v₂ = 1.28 m /s

Time allowed = 2 x 60

= 120 s

So maximum distance upto which she can remain away from spacecraft

= 120 x 1.28

= 153 m .

b )

The Newton's law which explains the theory behind it is "third law of motion" . This law gives law of conservation of momentum .

bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-03-02T10:55:50+01:00

The maximum distance an astronaut can be from the craft and still return within 2.00 min is 153 m.

What is Newton’s law of motion?

Newton’s law of motion states that the rate of change of the moment of an object is equal to the magnitude of the force and the direction of the force acting on the object.

By the law of conservation of momentum for two bodies,

[tex]m_1v_1=m_2v_2\\[/tex]

Here, (m) is the mass of the body and (v) is the velocity of the body..

(a) The maximum distance an astronaut can be from the craft and still return within 2.00 min-

The astronaut, through the oxygen tank, an opposite force act towards her body with equal magnitude.

The speed of the tank is 8 m/s away from the spacecraft. As, the mass of the tank is 12 kg and mass of the astronaut is 75 kg (87-12). Thus, by the law of conservation the speed of the astronaut is,

[tex]12\times8=75\times v_a\\v_a=1.28\rm m/s[/tex]

Now the time is 2 min (120 seconds). Thus, the maximum distance an astronaut can be from the craft is,

[tex]d=1.28\times120\\d=153\rm m[/tex]

(b) Newton's laws of motion about this strategy.

The newton's laws of motion says that for every action, there is an equal and opposite reaction. As the astronaut, through the oxygen tank, an opposite force act towards her body with equal magnitude.

Learn more about the Newton’s law of motion here;

https://brainly.com/question/25545050