Provincial Exam: Simple momentum explosion question

[Senjai]

Homework Statement

A 1.0kg physics puck is at rest when a small explosion breaks it into three pieces. A 0.50 kg piece, goes north at 10 m/s, a .3 kg piece goes east at 20 m/s. What is the magnitude of the momentum of the third piece.

Homework Equations

$$p = mv$$
Momentum Before = Momentum After

The Attempt at a Solution

So i know that the momentum before is zero, so the sum of the momentum on the x-axis is zero, and the sum on the y-axis is zero.

Because the first two pieces are at right angles to each other, i calculated the net momentum, or their resultant, and stated that the momentum of the third piece should be equal and opposite to maintain the law of momentum conservation.

So i determined: the first piece had a momentum of 5 kg m/s north, the second, 6 kg m/s east.

Plugged the values into the pythagorean theorum and got 7.8 kg m/s..

Which is an answer on the sheet, but it's wrong. The correct answer is 3.3 kg m/s

Could anyone tell me where i went wrong??

Regards,
Senjai

 

[Senjai]

*bump* :(