Conservation of Momentum Question Involving Two-Dimensions

[omgbeandip]

Homework Statement

A grenade is rolling due west at 0.954m/s along a floor when it explodes into three pieces of equal mass. The first piece moves at 3.6m/s, 20° [N of W]. The second travels at 5.8m/s, 62° [S of W]. Calculate the velocity of the third piece.

Homework Equations

P=mv
PBefore=Pafter
a^2 + b^2= c^2
Tan^-1 to find angle

The Attempt at a Solution

My attempt is in the attached image. I was curious if my masses were correct. Since they are all equal, I inputted 1 as my before component, and 1/3 for the 3 after components. Is this correct? And, are my calculations correct as well?[/B]

 

[Orodruin]

Regarding the masses: You could simply assume that the grenade has a total mass $m$, which will make the parts have mass $m/3$. You will notice that $m$ cancels out of the final answer and thus that it does not matter what you chose for $m$. In particular, $m = 1\,\rm kg$ should give the correct answer just as well as any other mass.

 

[WhosUrDaddy]

Homework Statement

A grenade is rolling due west at 0.954m/s along a floor when it explodes into three pieces of equal mass. The first piece moves at 3.6m/s, 20° [N of W]. The second travels at 5.8m/s, 62° [S of W]. Calculate the velocity of the third piece.

Homework Equations

P=mv
PBefore=Pafter
a^2 + b^2= c^2
Tan^-1 to find angle

The Attempt at a Solution

My attempt is in the attached image. I was curious if my masses were correct. Since they are all equal, I inputted 1 as my before component, and 1/3 for the 3 after components. Is this correct? And, are my calculations correct as well?[/B]

I don't think you should put the mass as 1/3 since that would create the assumption that the original mass is 1kg. Just look at the velocities. When they tell you that the masses are equal, it implies that the mass is negligible, so do the exact same calculations you have done already and simply remove the (1/3).

 

[kuruman]

When they tell you that the masses are equal, it implies that the mass is negligible, so do the exact same calculations you have done already and simply remove the (1/3).

There is no implication of the sort. "Negligible" mathematically means "very small" (i.e. can be considered zero) by comparison with something else. There is no such comparison here as the three fragments have the same mass.