An unstable atomic nucleus of mass 1.84 x 104 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.10 x 10 kg., moves in the y direction with a speed of 6.00 x 10° m/s. Another particle, of mass 8.44 x 10 kg. moves in the x direction with a speed of 4.00 x 10° m/s. (a) Find the velocity of the third particle. i) m/s (b) Find the total kinetic energy increase in the process.
An unstable atomic nucleus of mass 1.84 x 104 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.10 x 10 kg., moves in the y direction with a speed of 6.00 x 10° m/s. Another particle, of mass 8.44 x 10 kg. moves in the x direction with a speed of 4.00 x 10° m/s. (a) Find the velocity of the third particle. i) m/s (b) Find the total kinetic energy increase in the process.
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![### Physics Problem: Particle Disintegration
An unstable atomic nucleus of mass \(1.84 \times 10^{-26}\) kg initially at rest disintegrates into three particles. One of the particles, of mass \(5.10 \times 10^{-27}\) kg, moves in the \(x\) direction with a speed of \(4.00 \times 10^6\) m/s. Another particle, of mass \(8.44 \times 10^{-27}\) kg, moves in the \(y\) direction with a speed of \(6.00 \times 10^6\) m/s.
**(a)** Find the velocity of the third particle.
\[
(\_\_\_ \, \text{i} + \_\_\_ \, \text{j}) \, \text{m/s}
\]
**(b)** Find the total kinetic energy increase in the process.
\[
\_\_\_ \, \text{J}
\]
This exercise involves calculation of both conservation of momentum and kinetic energy in a disintegration process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc618d345-2f4b-4ba3-b2cb-33f4f1942e28%2Fa1d4f536-149a-42c2-add5-5eeaa0c84f55%2F1qpnnxf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Physics Problem: Particle Disintegration
An unstable atomic nucleus of mass \(1.84 \times 10^{-26}\) kg initially at rest disintegrates into three particles. One of the particles, of mass \(5.10 \times 10^{-27}\) kg, moves in the \(x\) direction with a speed of \(4.00 \times 10^6\) m/s. Another particle, of mass \(8.44 \times 10^{-27}\) kg, moves in the \(y\) direction with a speed of \(6.00 \times 10^6\) m/s.
**(a)** Find the velocity of the third particle.
\[
(\_\_\_ \, \text{i} + \_\_\_ \, \text{j}) \, \text{m/s}
\]
**(b)** Find the total kinetic energy increase in the process.
\[
\_\_\_ \, \text{J}
\]
This exercise involves calculation of both conservation of momentum and kinetic energy in a disintegration process.
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