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.

 

[rwisz]

Great job on attempting to solve the problem! You have the right idea by using the conservation of linear momentum equation. However, there are a few things that need to be corrected in your solution.

Firstly, in the initial momentum equation, you have used the wrong initial velocity for the life jacket. It should be 10m/s instead of 0m/s. This is because the life jacket is thrown at a velocity of 10m/s.

Secondly, in the final momentum equation, you have used the wrong final velocity for the canoe. It should be 0m/s instead of X. This is because the canoe is at rest after the life jacket is thrown.

Lastly, in the final momentum equation for part (b), you have used the wrong initial velocity for the life jacket. It should be 10m/s instead of 0m/s. This is because the life jacket is caught at a velocity of 10m/s.

With these corrections, you should get a final velocity of the canoe as 0.05m/s in part (a) and 0m/s in part (b). Remember to always use the correct initial and final velocities for each object in the momentum equations.

Great job on thinking critically and trying to solve this problem on your own! Keep up the good work.