The answers to your questions are as listed below
A) The total momentum of the system is : < - 167, 133, 87 > kg m/s
B) Velocity of the center of mass of this system : < - 10.44 , 8.31, 5.44 > m/s
C) Total kinetic energy of the system : 5159.5 J
D) Translational kinetic energy of the system : 1660.84 J
E) kinetic energy relative to the center of mass : 3498.66 J
<u>Given data : </u>
m₁ = 4 kg , V₁ = < 10, -5, 15 > m/s
m₂ = 9 kg, V₂ = < -15, 5, -3 > m/s
m₃ = 3 kg V₃ = < -24, 36, 18 > m/s.
<h3>A) Determine the total momentum of the system </h3>
Total momentum = Σ mv
= < 4*10 + 9*(-15) + 3*(-24), 4*(-5) + 9*5 + 3*36, 4*15 + 9 (-3) + 3*18 >
= < - 167, 133, 87 > kg m/s
<h3> B) Velocity at the center of mass of this system </h3>
Velocity = < - 167 / 16 , 133/ 16, 87/ 16 >
= < - 10.44 , 8.31, 5.44 > m/s
<h3>C) Determine the total kinetic energy of the system </h3>
Total Kinetic energy = 1/2 m₁v₁² + 1/2 m₂v₂² + 1/2 m₃v₃² --- ( 1 )
where : v² = v₁² + v₂² + v₃²
therefore
Total kinetic energy = 700 + 1165.5 + 3294
= 5159.5 J
<h3>D) Determine the translational kinetic energy of the system </h3>
Translational kinetic energy ( Kcm ) = 1/2 ( m₁ + m₂ + m₃ ) * Velocity²
= 1/2 ( 16 ) * ( - 10.44² + 8.31² + 5.44² )
Hence translational kinetic energy = 1660.84 J
E) The Kinetic energy of the system relative to the center of mass
Krel = Ktotal - Kcm
= 5159.5 - 1660.84
= 3498.66 J
Hence we can conclude that the answers to your questions are as listed above.
Learn more about Translational kinetic energy :brainly.com/question/25959744
