Solving for the Third Fragment's Speed Using Momentum and Collision Equations

[Neerolyte]

A 32.0-kg body is moving in the direction of the positive x-axis with a speed of 215 m/s when, owing to an internal explosion, it breaks into three pieces. One part, whose mass is 7.0 kg, moves away from the point of explosion with a speed of 310 m/s along the positive y axis. A second fragment, whose mass is 4.5 kg, moves away from the point of explosion with a speed of 370 m/s along the negative x axis. What is the speed of the third fragment? Ignore effects due to gravity.

Can't seem to get this right

M1 = 7.0kg
M2 = 4.5kg
M3 = Mtotal - (M1+M2)

Isn't it simply adding up momentum vector of M1, and momentum vector of M2 then the
resultant will be momentum of M3?

If so, then you get a right angle triangle.

You know momentum of both sides and just by using pythagoras you can find
momentum of M3, then just divided by the mass then you can get the velocity right?

 

[ehild]

Can't seem to get this right
M1 = 7.0kg
M2 = 4.5kg
M3 = Mtotal - (M1+M2)
Isn't it simply adding up momentum vector of M1, and momentum vector of M2 then the
resultant will be momentum of M3?

You have to subtract the resultant from the original momentum vector of the bullet to get M3.

ehild

 

[Neerolyte]

I'm not really sure what you mean by that, could you explain it again thanks

 

[ehild]

I'm not really sure what you mean by that, could you explain it again thanks

Sorry I did not notice your formula M3 = Mtotal - (M1+M2) before. I wanted to say the same - you should subtract the resultant of M1 and M2 from Mtotal to get M3, and I ment that Mtotal is momentum of the bullet before exploding.

M3 = Mtotal - (M1+M2).

ehild

 

[Neerolyte]

hm...Okay..i think this problem should be solve by components, but can i have some hints on how to use component methods?

 

[lostdaytomorrow]

Use conservation of momentum...?

 

[ehild]

hm...Okay..i think this problem should be solve by components, but can i have some hints on how to use component methods?

The total momentum which is equal to the momentum the bullet had just before the explosion is 32*215i as the piece moves along the positive x axis. The momentum of the 7 kg piece is 7*310j as the piece moves along the positive y axis. The momentum of the 4.5 kg piece is -4.5*370i.
The sum of the x components is the same before and after explosion, and the same holds for the y components.
32*215=M3x-4.5*370
0=M3y+7*310.
Calculate the components of M3. Determine the magnitude and divide by the mass of the third piece to get the speed as you have written down in your first letter.
ehild