On a frictionless air table in the lab you measure the velocities of two blocks as  v1 = (3i+ 3j) m/s, and v2 = (3i−3j) m/s. The masses of the blocks are m1 = 2kg and m2 = 1kg. The initial positions of the two blocks are r1,0 = i m and r2,0 = (i + 6j) m.

(a) What are the vector positions of the two particles, r1(t) and r2(t) as they move across the table?

(b) What is the position of the center of mass as a function of time, rcm(t)?

(c) What is the velocity of the center of mass Vcm ?

(d) Draw the trajectories of both blocks and of the center of mass.

(e) What are the velocities of the two blocks with respect to the center of mass:

v1,cm = v1 − Vcm =? and similarly for block 2.

(f) What is the momentum of each block with respect to the center of mass?

(g) What is the position of each block with respect to the center of mass, as a function of time?

(h) Draw the trajectories of the blocks as seen from the center of mass.

(i) Draw the momentum vectors measured by someone moving with the center of mass.

(j) When will the two blocks collide?

(k) What is the total kinetic energy?

(l) The collision is elastic. How do the two blocks move after the collision?