Ice skator throwing gloves to mvoe

[JayHakimi1]

Homework Statement

An amateur skater of mass M is trapped in the middle of an ice rink and is unable to return to the side where there is no ice. Every motion she makes causes her to slip on the ice and remain in the same spot. She decides to try to return to safety by throwing her gloves of mass m in the direction opposite the safe side.

If she does move, calculate her velocity v-girl relative to the Earth after she throws the gloves, otherwise enter 0. (Use the following as necessary: m, M, and v-gloves).

Homework Equations

change in momentum = final momentum - initial momentum

The Attempt at a Solution

using the equation above i got that

v→ girl = (m/M) v→gloves

(i tried to show that its a vector above.)

but the answer is wrong, any suggestions?

 

[grzz]

What is the initial momentum?

 

[JayHakimi1]

its not given, you have to solve the velocity using variable. No number involved

 

[grzz]

Let us assume that the skater is initially at rest.
Then what is the initial momentum?

 

[JayHakimi1]

it would be zero

 

[grzz]

Correct.
Then what is the final momentum?

 

[JayHakimi1]

either 0 or M v girl

 

[grzz]

If the initial momentum was 0, what does the Principle of Conservation of Momentum tell us?

 

[JayHakimi1]

That the final momentum has to equal to zero?

 

[grzz]

Correct!
So the momentum of the girl must be equal in magnitude and opposite in direction to that of the glove.

 

[JayHakimi1]

so it like thi

v girl = -(m glove* v glove)/m girl

right?

 

[grzz]

right.

 

[JayHakimi1]

but the website says that answer is wrong. IDK why tho

 

[grzz]

The Physics I know tells me that if the total initial momentum of system in a certain direction is zero then the final total momentum in that direction is zero also so long as there are no resultant forces on the system in that given direction.

So the momentum of the girl must be equal in magnitude and opposite in direction to that of the glove.