   Chapter 6, Problem 29P

Chapter
Section
Textbook Problem

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 (Fig. P6.29).(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 works. Figure P6.29

(a)

To determine
Distance moved by the Astronaut

Explanation

Given Info: Total mass of the Astronaut is mA=ms+mt=87.0 kg , mass of the tank is mt=12.0kg , mass of the  astronaut alone is ma=75kg .

Explanation:

Choose positive direction towards the spacecraft, velocity of the tank, Vtf=8.00m/s , initially velocities of the tank and astronaut are vai=vti=0

Apply conservation of momentum to astronaut-tank system

(mava+mtvt)i=(mava+mtvt)f (1)

• ma is the mass of the astronaut
• mt is the mass of the tank
• va is the velocity of the astronaut
• vt is the velocity of the tank

Rewrite the above equation with initial velocities as zero

(mava+mtvt)f=0mavaf=mtvtfvaf=(mtma)vtf (2)

Substitute 12

(b)

To determine
The movement of astronaut by Newton’s law of motion.

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