Solving for Velocity in a Three-Piece Explosion

[ElectricMile]

A firecracker in a coconut blows the coconut into three pieces. Two pieces of equal mass fly off south and west, perpendicular to each other, at 20 m/s. The third piece has twice the mass as the other two.What is the speed of the third piece?

really boggled, no masses are given? i thought since the mass is double then the speed would be half of the speed of the 1st and 2nd pieces? anyone have an equation to help me out?
thanks

 

[vsage]

Resolve the momentums in the X and Y directions assuming the body is initially at rest:

$$\sum m_i v_i = 0$$ Here's the X direction (assuming east/west are the postive/negative x axis):

$$-20m + 2mv_x = 0$$

and in the Y direction:

$$-20m + 2mv_y = 0$$

It's easy to see what $$v_x$$ and $$v_y$$ are.

 

[ElectricMile]

still don't understand, what do i put for the masses?

 

[ZedLeppelin]

It doesn't matter what the masses are. The ratios are given. The masses will cancel out later once you have the relationship worked out.

 

[ElectricMile]

so Vx = 10 and Vy = 10? after i solved in the equations