Calculating Original Speed of Exploding Mess Kit

[rosstheboss23]

A 8.0 kg mess kit sliding on a frictionless surface explodes into two 4 kg parts, one moving at 2.5 m/s, due north, and the other at 4.5 m/s, 30° north of east. What was the original speed of the mess kit?

Known equations:
PM= p1m1+p2m2

I tried to give this question a shot but to no avail. I tried to switch the axis to make the problem easier, but still got the wrong answer. 8(unknown velocity) = 4(4.5kg)(cos60) + 4(2.5)cos0 adn I got 2.375m/s, but this wasn't right...so I tried it from the same perspective on the y-axis 8(unknown velocity in y direction) = 4(4.5kg)sin60 + 4(2.5)sin0(this drops off) and got 1.9485m/s...this wasn't the same as the other velocity so I know I am doing something wrong...any pointers?

 

[Doc Al]

I tried to give this question a shot but to no avail. I tried to switch the axis to make the problem easier, but still got the wrong answer. 8(unknown velocity) = 4(4.5kg)(cos60) + 4(2.5)cos0 adn I got 2.375m/s, but this wasn't right...

That gives you one component of the velocity (assuming your arithmetic is correct).

so I tried it from the same perspective on the y-axis 8(unknown velocity in y direction) = 4(4.5kg)sin60 + 4(2.5)sin0(this drops off) and got 1.9485m/s...

That gives you the other component.

In summary:

Find the components of the total momentum: x-components (east) and y-components (north). Once you have the components of the total momentum and then the components of the original velocity, then you can find the magnitude.

 

[rosstheboss23]

So I found the components of the total momentum, but how would I relate that back to the original momentums of the problem to find the velocity of the 8kg messkit? Would I add the x and y direction momentums (p=19 for x) and (p=15.588 for y) and then divide by 8?...when I did that I got 4.324m/s for the initial 8kg mass's velocity. I'm not sure if that is right though.

 

[Doc Al]

So I found the components of the total momentum, but how would I relate that back to the original momentums of the problem to find the velocity of the 8kg messkit? Would I add the x and y direction momentums (p=19 for x) and (p=15.588 for y) and then divide by 8?...when I did that I got 4.324m/s for the initial 8kg mass's velocity. I'm not sure if that is right though.

Do like this: Find the x- and y-components of the momentum of each 4 kg piece. Add the x-components up to get the x-component of the total momentum, which is the x-component of the original momentum; use that to find the x-component of the original velocity. Do the same thing for the y-components to find the y-component of the original velocity.

Once you have the components of the velocity vector, find the magnitude like any other vector: Use the Pythagorean theorem.

 

[rosstheboss23]

Infinite thank yous. :)