What is the speed of the third fragment in an exploding object problem?

[SnowOwl18]

Alrighty, here is a problem I am stuck on.

----A 21.0-kg body is moving in the direction of the positive x-axis with a speed of 274 m/s when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 7.5 kg, moves away from the point of explosion with a speed of 428 m/s along the positive y axis. A second fragment, whose mass is 3.5 kg, moves away from the point of explosion with a speed of 483 m/s along the negative x axis. What is the speed of the third fragment? Ignore effects due to gravity.-----

Ok...so the momentum in the positive x direction before the explosion was p=mv...or 21x274= 5754 kg*m/s...i think the y direction is irrelevant in the problem, since momentum in the x-axis is conserved...so assuming that, i do the equation 3.5kg x (-483 m/s) + 10kg x V3 = 5754 kg*m/s...the 2nd fragment's velocity is negative because it goes along the negative x axis...and the third fragment's mass is 10kg because 21-7.5-3.5 = 10kg. Anyway, I solved for the third fragment's velocity (V3) and got an answer of 744.45 m/s...but the computer program says I'm wrong. Does anyone know what I'm doing incorrectly? And if so, how do I go about the problem the correct way? Thanks so much. :D

 

[arildno]

The momentum in the y-direction is definitely relevant; it is to be zero before and after the explosion..

 

[SnowOwl18]

hmm..I'm not sure how to incorporate that though. I can find the velocity of the 3rd fragment in the y direction...(7.5 x 428) + 10x = 0...and I get -321 m/s. So...if I have the speed in the x component (744.45m/s) and in the y component (-321m/s)...how I do I find the fragment's speed? I'm not sure what I should be doing with that... :/


ohhh...duh. I'm so dumb today. I just figured it out...do it like a triangle...744.45^2 + (-)321^2 = V^2...ha. Thanks a bunch!