Physics final speed problem

[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...

 

[m2003]

Your attempt at solving the problem using the conservation of linear momentum is correct. However, the final speed of the astronaut will depend on the direction of the tool kit's velocity as seen from the shuttle.

If the 6 m/s velocity is in the same direction as the astronaut's initial velocity (toward the shuttle), then it will be considered a positive velocity. This would result in a final speed of 1 m/s, as you calculated.

If the 6 m/s velocity is in the opposite direction as the astronaut's initial velocity (away from the shuttle), then it will be considered a negative velocity. This would result in a final speed of 4 m/s, as you calculated.

Therefore, the correct answer would depend on the direction of the tool kit's velocity as seen from the shuttle. Without this information, it is not possible to determine the final speed of the astronaut.