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

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The discussion centers on calculating the increase in kinetic energy during the disintegration of an unstable atomic nucleus. The nucleus, initially at rest, breaks into three particles, with two particles' masses and velocities provided. The third particle's velocity is determined to be (-1.40e7 i - 1.26e7 j). Participants are seeking assistance to accurately compute the total kinetic energy increase resulting from this disintegration. Help is requested as the original poster is close to exhausting their attempts to solve the problem.
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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