Solving the Firework Exploding Homework Statement

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Homework Help Overview

The problem involves a firecracker that explodes into three pieces at its highest point, with two pieces moving at right angles to each other. The question seeks to determine the speed of the third piece using principles of momentum conservation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the conservation of momentum, noting that the initial momentum is zero and questioning how this affects the final momentum. There are attempts to set up equations for the momentum of each piece, with some participants recognizing the need to consider vector components.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to the problem. Some guidance has been offered regarding the treatment of momentum as a vector quantity, and there is acknowledgment of the need to balance the momentum of the pieces in a vector sense.

Contextual Notes

Participants are working under the assumption that the masses of the pieces are equal and that the explosion occurs at the peak of the firecracker's trajectory. There is a noted challenge in handling the vector nature of momentum in the calculations.

JJones_86
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Homework Statement


A firecracker is tossed straight up into the air. It explodes into three pieces of equal mass just as it reaches the highest point. Two pieces move off at 130 m/s at right angles to each other. How fast is the third piece moving?


Homework Equations


P = m*v
Pi = Pf

The Attempt at a Solution



So the initial momentum is 0 because it is not moving when it explodes, so doesn't that mean that final momentum is 0 because of the conservation of momentum? I tried this, but I'm not getting the right answerl...
 
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JJones_86 said:

Homework Statement


A firecracker is tossed straight up into the air. It explodes into three pieces of equal mass just as it reaches the highest point. Two pieces move off at 130 m/s at right angles to each other. How fast is the third piece moving?


Homework Equations


P = m*v
Pi = Pf

The Attempt at a Solution



So the initial momentum is 0 because it is not moving when it explodes, so doesn't that mean that final momentum is 0 because of the conservation of momentum? I tried this, but I'm not getting the right answerl...

What you have are two vectors at right angles. You are right about momentum being conserved. Hence you have the third momentum that must balance the first 2.
 
Ok here is my attempt at a solution

Particle 1
P = m * v
P = m * 130 m/s

Particle 2
P = m * v
P = m * 130 m/s

Particle 3(Unknown)
P = m * v

----------------------
So in order for it to equal 0 I used this equation...

P1 + P2 + P3 = 0
m(130 m/s) + m(130 m/s) + m*v = 0

So I'm obviously using the wrong equation because of the two unknowns..
 
JJones_86 said:
Ok here is my attempt at a solution

Particle 1
P = m * v
P = m * 130 m/s

Particle 2
P = m * v
P = m * 130 m/s

Particle 3(Unknown)
P = m * v

----------------------
So in order for it to equal 0 I used this equation...

P1 + P2 + P3 = 0
m(130 m/s) + m(130 m/s) + m*v = 0

So I'm obviously using the wrong equation because of the two unknowns..

What you failed to do is treat the vectors by their x,y components.

Your equation is not a scalar equation, it is a vector equation.

[tex]\vec P_1 + \vec P_2 + \vec P_3 = 0[/tex]
 
Ok, I got it now, Thank you very much!
 

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