How Does Throwing a Toolkit Affect an Astronaut's Speed in Space?

[Confused_07]

Homework Statement

80 kg astronaut carrying a 20kg tool kit is initially drifting toward a stationary space shuttle with a speed of 2 m/s. If sh throws the tool ki toward the shuttle with a speed of 6 m/s as seen from the shuttle, her final speed is?

Homework Equations

If it is seen from the shuttle, does that mean the 6 m/s is a negative or a positive?

The Attempt at a Solution

I used the Conservation of Linear Momentum

m1Vf1 + m2Vf2 = m1Vo1 + m2Vo2

Vf1 = (m1Vo1 + m2Vo2 - m2Vf2) / m1

= [(80*2) + (20*2) - (20*6)] / 80
= 1 m/s

**If I use a -6 instead, the answer is 4 m/s. Which is right?

 

[olgranpappy]

Homework Statement

80 kg astronaut carrying a 20kg tool kit is initially drifting toward a stationary space shuttle with a speed of 2 m/s. If sh throws the tool ki toward the shuttle with a speed of 6 m/s as seen from the shuttle, her final speed is?

Homework Equations

If it is seen from the shuttle, does that mean the 6 m/s is a negative or a positive?

The Attempt at a Solution

I used the Conservation of Linear Momentum

m1Vf1 + m2Vf2 = m1Vo1 + m2Vo2

Vf1 = (m1Vo1 + m2Vo2 - m2Vf2) / m1

= [(80*2) + (20*2) - (20*6)] / 80
= 1 m/s

**If I use a -6 instead, the answer is 4 m/s. Which is right?

one is correct and one is incorrect. but which? Let me do this dumb Socratic thing and lead you to the answer by asking you questions...

Why did you choose the initial velocity as positive? Why not use v0=-2m/s?

Does the overall sign really matter? (I'll answer that..) No.

You just have to make sure that the signs are consistent. If you choose to call the initial velocity positive (i.e. +2m/s) and the toolbox is moving in that same direction that you called positive, well, then...