Mass & Velocity Components of Third Fragment in Exploding Shell | 0.4kg Shell

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In a gravity-free environment, a 0.4 kg shell explodes into three fragments, with two fragments having known masses and velocity components. The first fragment has a mass of 0.12 kg with velocity components of 25 m/s in the x-direction and 58 m/s in the y-direction, while the second fragment has a mass of 0.04 kg with velocity components of -7.5 m/s in the x-direction and 13 m/s in the y-direction. To find the mass and velocity components of the third fragment, conservation of momentum must be applied, ensuring that the total momentum before and after the explosion remains equal. The total mass of the fragments must equal the original mass of the shell, and the momentum in both x and y directions must be conserved. The calculations will yield the mass and velocity components of the third fragment.
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A shell of mass 0.4 kg is at rest in a gravity-free environment when it suddenly explodes into three fragments. The mass and x,y components of two of the fragments is given in the table:particle mass (kg) vx (m/s) vy (m/s)

[1] 0.12 25 58

[2] 0.04 -7.5 13

[3] ? ? ?
particle 1 : .12 [mass] ; 25 [vx (m/s)] ; 58 [vy (m/s)]
particle 2 : .04 [mass] ; -7.5 [vx (m/s)] ; 13 [vy (m/s)]
particle 3 : ? [mass] ; ? [vx (m/s)] ; ? [vy (m/s)]Find the mass and x,y components of the velocity of the third fragment.
 
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Use the appropriate conservation law.

ehild
 

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