An astronaut in her space suit has a total mass of m 1 = 79.5 kg, including suit

Question

An astronaut in her space suit has a total mass of m1 = 79.5 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 oxygen tank of mass m2 = 12.0 kg away from her spacecraft with a speed v = 7.00 m/s to propel herself back toward it

a) Determine the maximum distance she can be from the craft and still return within 2.20 min (the amount of time the air in her helmet remains breathable).
m

Explanation / Answer

Momentum conservation

Initial momentum = 0

So final momentum = 0

m2 v - (m1-m2) u = 0

12 *7 - (79.5-12)*u = 0

u = 12*7/(79.5-12) = 1.244 m/s ( in opposite dirction )

Speed of astronaut = u = 1.2444 m/s

Maximum time she has = T = 2.2 min = 2.2 x 60 = 132 s

Maximum distance = D = T*u = 132*1.2444 = 164.26 m

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maximum distance she can be from the craft = 164.26 m

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