An astronaut in her space suit has a total mass of m_1 = 83.5 kg, including suit

Question

An astronaut in her space suit has a total mass of m_1 = 83.5 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 or mass m_2 = 12.0 kg away from her spacecraft with a speed v = 8.50 m/s to propel herself back toward it (see figure). Determine the maximum distance she can be from the craft and still return within 2.40 min (the amount of time the air in her helmet remains breathable). m Explain in terms of Newton's laws of motion why this strategy works.

Explanation / Answer

a)
let v is the speed of astronaut

apply conservation of moemntum

(83.5 - 12)*v = 12*8.5

==> v = 12*8.5/(83.5 - 12)

= 1.4266 m/s

distance travelled during 2.4 min,

d = v*t

= 1.4266*2.4*60

= 205 m

b) According to Newton's third law, when the astronaut exerts force on cyllinder, the cyllinder also exerts the same amount of force on austronaut.

so, the cyllinder gets momentum towards +x axis and the austronaut gets the same amount of momentum towards -x direction.

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