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Chapter 1: Q16E (page 264)

A 68.5 kg astronaut is doing a repair in space on the orbiting space station. She throws a 2.25 kg tool away from her at 3.20 m/s relative to the space station. With what speed and in what direction will she begin to move?

Short Answer

Expert verified

Thus, the velocity away from the tool is 0.105m/s.

Step by step solution

01

Given in the question.

Mass of tool ismt=2.25kg

Mass of astronaut is ma=68.5kg.

Velocity of tool after the throw is vt=3.20m/s.

Velocity of astronaut after the throw is va.

02

Law of conservation of momentum.

Use the law of conservation of momentum which states that the momentum of the bodies before collision is equal to the sum of the momentum of the bodies after collision. After collision, the bodies will move with a common velocity v.

03

The velocity astronaut is calculated.

Use the conservation of angular momentum to obtain the velocity of the astronaut:

0=mtvt+mavamava=-mtvtva=-mtvtma=-2.25×3.2068.5≈-0.105m/s

Negative sign means that the direction of this velocity to the direction of tool’s velocity.

Hence, the velocity away from the tool is 0.105 m/s.

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