Answer:
The speed is -0.105m/s and the direction of this velocity stands opposite to the direction of the tool's velocity.
Explanation:
Conservation of momentum is the general law of physics according to which the quantity called momentum that represents motion never changes in an isolated group of objects; that exists, the total momentum of a system stays constant.
Using the momentum conservation law, get:
[tex]$$0=m_{t} v_{t}+m_{a} v_{a}$$[/tex]
where conveys the momentum before she throws the tool, [tex]$m_{t}=2.25 \mathrm{~kg}, m_{a}=68.5 \mathrm{~kg}$[/tex] exists the masses of the tool and astronaut respectively,
[tex]$v_{t}=3.20 \mathrm{~m} / \mathrm{s}, v_{a}$[/tex] exists the velocities of the tool and astronaut after the throw.
Expressing [tex]$v_{a}$[/tex], obtain:
[tex]v_{a}=-\frac{m_{t} v_{t}}{m_{a}} \\[/tex]
[tex]v_{a}=-\frac{2.25 \mathrm{~kg} \cdot 3.20 \mathrm{~m} / \mathrm{s}}{68.5 \mathrm{~kg}} \approx-0.105 \mathrm{~m} / \mathrm{s}[/tex]
Sign "-" indicates that the direction of this velocity stands opposite to the direction of the tool's velocity.
Hence, The answer is -0.105m/s.
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