Conceptual Question - Newton's Second Law

[PeachBanana]

Homework Statement

An astronaut is taking a space walk near the shuttle when her safety tether breaks. What should the astronaut do to get back to the shuttle?

Attempt to "swim" toward the shuttle.
Take slow steps toward the shuttle.
Take a tool from her tool belt and throw it away from the shuttle.
Take the portion of the safety tether still attached to her belt and throw it toward the shuttle.


What I don't understand:

Assuming that the astronaut can throw any tool with the same force, what tool should be thrown to get back to the shuttle as quickly as possible?
The tool with the smallest mass.
The tool with the largest mass.
Any tool, since the mass of the tool would make no difference

Homework Equations

F = ma

The Attempt at a Solution

This is from Online Homework and you can look at hints. I looked at one and this is what it said:

Newton's 2nd law states that . If force is held constant, then acceleration is inversely proportional to mass. For example, when the same force is applied to objects of different mass, the object with the largest mass will experience the smallest acceleration.

So is this saying the actual large tool will not accelerate quickly in comparison to the acceleration that the astronaut would feel because her mass is smaller? I just don't think I have a good grasp of this concept.

 

[tiny-tim]

Welcome to PF!

Hi PeachBanana! Welcome to PF!

So is this saying the actual large tool will not accelerate quickly in comparison to the acceleration that the astronaut would feel because her mass is smaller?

I'm not sure whether, when it says "when the same force is applied to objects of different mass" it means
i] the astronaut applying the same force to two different tools, or
ii] the same (equal and opposite) forces between the astronaut and one tool.

What you've written is correct, as an answer to ii]

But the question is more about situation i], isn't it?