Question

An astronaut in her space suit has a total mass of 87.0 kg, 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 12.0 kg 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 within 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 work

Answer 1

a )

given data:

m1 = 12 kg

m2 = 87-12 = 75 kg

v1 = 8m/s

v2 =? we have to calculate.

both astronaut and her oxygen tank will float in space because of weightnless.

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 .

So, conservation of momentum-----

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 .