Linear Momentum (One Dimension) Quiz Question

[LeonGrande]

Hello forum, today in my gr. 12 physics class I had a interesting question which I could not prove at all for the life of me. It is a really simple question, just with a little twist I suppose. As I was driving home from class I was thinking about what I was missing and thought up a solution. Anyways I'll state the question and all that jazz...

1. Two people are sitting in a canoe which sits in the middle of a lake. Both individuals have a mass of 75kg, and the canoe itself has a mass of 50kg. The canoe is not moving, nor are the people sitting inside. Person 1 decides to throw to Person 2 a life jacket (edit: life jacket has a mass of 1kg) at 10m/s [E].

Calculate the theoretical velocity of the canoe while the life jacket is still in mid air.

Also,

Calculate the velocity of the canoe after person 2 catches the life jacket.

Side note... the question was not worded at all like this, it was much more confusing! lol

Homework Equations

m1*v1o+m2*v2o=m1*v1f+m2*v2f

v=velocity
m=mass
o=initial, f=final

The Attempt at a Solution

So here is my attempt at a solution,

(a) (1kg)*(0m/s)+(200kg)*(0m/s)=(1kg)*(10m/s)+(200kg)*(X)
X= -0.05m/s

(b) (1kg)*(10m/s)+(200kg)*(-0.05m/s)=(1kg)*(0m/s)+(200kg)*(X)
X= 0m/s

...So there it is. I was not to sure whether or not I should have combined the masses or not.

Sorry for any typos, I just got home and am drained. Thanks for any help!

 

[kuruman]

Hi LeonGrande and welcome to PF.

Without the mass of the life jacket one cannot solve this. Looking at your solution, it is correct if the mass of the jacket is 1 kg. You seem to know what you're doing.

 

[LeonGrande]

Yeah, sorry, the mass of the jacket is 1kg... >_>

Thanks for the quick reply! I guess I need to work on thinking clearly during tests/quizzes.

 

[kuruman]

Then you are OK.