I only need help with parts E, F, G, H, \& I please
Three spheres, \( A A, B B \), and \( C C \), are positioned on the \( x x \) axis as shown in (Figure 1). Spheres \( A A \) and \( B B \) are made of steel and have masses \( m A=m m A=m \) and \( m B=2 m m B=2 m \). Sphere \( C C \) is made of clay and has mass \( m C=m / 3 m C=m / 3 \). Initially, spheres BB and CC are at rest and sphere \( A A \) is moving in the positive xx direction with a speed vOvO . Then AA and BB undergo a head-on elastic collision, and later BB and CC collide and stick together. We will determine the velocities of each mass before and after the collisions in the lab frame and in the center-of-mass frame. All of your answers should be in terms of only vOvO or vO vO and mm . (a) Write down an expression for the initial center-of-mass velocity of the system before any collisions occur. (b) Determine the velocities of \( A A \) and \( B B \) just after the first collision. (c) Determine the velocities of BB and CC after the second collision. (d) Write down an expression for the final center-of-mass velocity of the system after all the collisions have occurred. (All of your answers should be in terms of only v 0 v 0 and mm .)
E. Determine the initial center-of-mass velocity of the system.
F. Determine the final velocity of sphere \( A A \) in the lab frame the moment after the first collision.
G. Determine the final velocity of sphere BB in the lab frame the moment after the first collision.
H. Use the relevant final velocities from the first collision as the initial velocities for the second collision and determine the final velocity of spheies BB and CC (they are moving together) after all the collisions.
I. Use the final velocities from Parts F, G, and H to calculate the final center-of-mass velocity of the system.