Calculating Fragment Speed in an Exploding Object

[chaotixmonjuish]

A 45.0-kg body is moving in the direction of the positive x-axis with a speed of 217 m/s when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 6.0 kg, moves away from the point of explosion with a speed of 349 m/s along the positive y axis. A second fragment, whose mass is 2.5 kg, moves away from the point of explosion with a speed of 346 m/s along the negative x axis. What is the speed of the third fragment? Ignore effects due to gravity.


I noticed right away that there might be components, so I came up with this:

X direction: 45*217=2.5*-346+36.5x x=291.23
Y direction: 45*217=6.0*349+36.5y y=210.15

then i plugged those two values into the pythagorean theorem. I get 359.14 m/s, however the computer says I'm wrong. Could someone help me?

 

[hage567]

Y direction: 45*217=6.0*349+36.5y y=210.15

If the object is initially moving in the x direction only, the initial momentum in the y direction is zero since there is no component of velocity in that direction.

 

[chaotixmonjuish]

whoops, thanks

296.82 m/s is what the corrected formula yielded.

The second part to the question is How much energy is released in the explosion? What is that exactly?

 

[hage567]

I would calculate the difference between the initial kinetic energy of the large mass, and the total kinetic energy of the three fragments after the explosion.

 

[chaotixmonjuish]

okay, cool

i go the right answer: 1.06x10^6 J

I was just confused about how I should treat it since it broke apart. This problem was surprisingly easy.