Percentage of Original KE that is Convertible

[Sunbodi]

Homework Statement

A 18-kg child is sliding on an icy surface toward her mother at 3.0 m/s. Her 62-kg mother starts toward her at 2.0 m/s, intending to catch her.

Homework Equations

KEi= (1/2) (m1)(v1)^2 + (1/2) (m2)(v2)^2
KEconv= (1/2)μ(v12)^2
μ= (m1m2)/(m1+m2)
v12= |v2 - v1 |

The Attempt at a Solution

KEi= 205 kJ
μ= 13.95 kg
v12 = 1 m/s
KEconv= 6.975

6.975/205= .034
Percent would be 3.4%, not sure what I'm doing wrong.

 

[billy_joule]

The problem statement appears incomplete, there's no question.

 

[haruspex]

v12 = 1 m/s

Is this supposed to be their relative velocity?

toward her mother

 

[jbriggs444]

The problem statement appears incomplete, there's no question.

@Sunbodi has used the sadly common approach of putting the question into the thread title and the details in the body of the first post. This is, of course, improper. The body of the message should contain everything the reader need to understand it. This applies in Physics Forums just as in all other forms of communication.

In this case we are asked for the "Percentage of Original KE that is Convertible".

The KE that is not recoverable in the collision would be the KE corresponding to the combined mass of the mother and child moving at the velocity of their combined center of mass. It is not recoverable because conservation of momentum requires this motion to remain. The least KE the system can have (barring external forces) is with mother and daughter both motionless in their combined center-of-mass frame.

 

[Sunbodi]

@jbriggs444 Thank you. It was a very stupid mistake of me to not add the question in the body of the message. It's my first thread and I created this account because of this stupid class that I'm in and this stupid stupid online site we're using to log our answers.

 

[Sunbodi]

Is this supposed to be their relative velocity?

That's what I meant however because it's an inelastic collision I also attempted to find their combined velocity using the conservation of momentum equation. That velocity would end up being: 2.225 m/s. The final answer in that would end up being .168 and the percent would be 16.8%. I typed in .168 earlier and it didn't have a notification that I had a significant figure error so I'm a bit afraid of typing in 16.8 as I only have 3 attempts remaining.

 

[Sunbodi]

I've solved the problem, it isn't 16.8% or 3.4% as those numbers are way too low and they'd make no sense at all. I made an error in calculating the relative velocity, if you need the actual solution and how I got there feel free to imbox me. Thanks to all of you kind souls who helped me solve this problem.