An astronaut in her space suit has a total mass of m1 = 87.5 kg, including suit

Question

An astronaut in her space suit has a total mass of m1 = 87.5 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 = 7.50 m/s to propel herself back toward it (see figure). (a) Determine the maximum distance she can be from the craft and still return within 1.80 min (the amount of time the air in her helmet remains breathable)

Explanation / Answer

a)

V = recoil velocity of the astronaut after throwing the cylinder

v = speed with which the cylinder was thrown

Vi = initial velocity of the system = 0

using conservation of momentum

m1 Vi = (m1 - m2) V + m2 v

0 = (87.5 - 12) V + 12 x 7.50

V = - 1.2 m/s

t = time of travel = 1.80 min = 1.80 x 60 = 108 sec

Distance travelled is given as

D = V t = 1.2 x 108 = 129.6 m

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