What is the increase in kinetic energy during an atomic nucleus disintegration?

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SUMMARY

The discussion focuses on calculating the increase in kinetic energy during the disintegration of an unstable atomic nucleus with a mass of 1.60 x 10-26 kg. The nucleus splits into three particles, with one particle (mass 5.08 x 10-27 kg) moving at 6.00 x 106 m/s along the y-axis and another particle (mass 8.50 x 10-27 kg) moving at 4.00 x 106 m/s along the x-axis. The velocity of the third particle is calculated to be (-1.40e7 i - 1.26e7 j) m/s. The total increase in kinetic energy from this disintegration process is the key outcome sought by the participants.

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albinoboy
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Problem: An unstable atomic nucleus of mass 1.60 10-26 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.08 10-27 kg, moves along the y-axis with a speed of 6.00 106 m/s. Another particle, of mass 8.50 10-27 kg, moves along the x-axis with a speed of 4.00 106 m/s.

A) Find the velocity of the third particle.

(-1.40e7 i - 1.26e7 j)

B) Find the total kinetic energy increase in the process.


I have been messing around with the numbers and can not figure out how to determine the increase in kinetic energy. I have one more attempt and then I get it wrong. Any and all help is greatly appreciated!
 
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