Calculating Relative Speed in One-Dimensional Collisions

[Pythagorean]

Collision in One Dimension?

Problem:

A 45kg girl is standing on a plank that has a mass of 150kg. The plant, originally at rest, is free to slide on a frozen, lake (flat, frictionless surface). The girl begins to walk along the plank at a constant speed of 1.5 m/s relative to the plank. What is her speed relative to the ice surface?

My Attempts:

Firstly, I tried m1v1=m2v2 thinking it was a simple momentum problem.

I later realized it was under collision in one-dimension, and judging by the deffinition, I assume it is an elastic collision.

So I continued on, both 'perfectly inelastic' and 'elastic' equations. In one example, I named v1 to be (1.5-v2), but now I'm so confused that I can't even rationalize which title the 1.5m/s belongs too. Is it v1 or is v1 1.5-v2?


Books Answers:

speed of plank: -.346 m/s
her speed relative to ground: 1.15 m/s

(this makes it obvious that her speed minus on the plank, plus the speed of the plank is her speed relative to the ground, but I'm still having problems setting this thing up.)

 

[Parth Dave]

I think you had it right the first time. It is a simple momentum problem. The momentum of the girl is 45(v + 1.5) where v is the velocity of the plank.

 

[Pythagorean]

I think you had it right the first time. It is a simple momentum problem. The momentum of the girl is 45(v + 1.5) where v is the velocity of the plank.

I finally figured it out. It actually ended up being a perfectly inelastic equation!

 

[pmrazavi]

You should assume all of the collisions to be inelastic, unless it's said that it's elastic.