A 26.0 g object moving to the right at 17.0 cm/s overtakes and collides elastically with a 10.0 g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision.

Question

a) 26.0 g object

b) 10.0 g object

Answer 1

The center of mass of the two objects moves to the right at a velocity
(26*17 + 10*15)/(26 + 10) = 16.44 m/s

Consider what happens in a coordinate system travelling the the CM.
a) The heavier object comes from the right at velocity 17-16.44 = 0.56 cm/s and leaves at -0.56 cm/s.
b) The lighter object approaches from the left at velocity 15 - 16.44 = -1.44 cm/s and leaves with velocity +1.44 m/s.

Transfering back to lab coordinate sytem (by adding +16.44 to both velocities) , the final velocity of the heavier object is -0.56 + 16.44 = 15.88 cm/s, and the lighter object is +1.44 + 16.44 =
17.88 cm/s.

The above is a shortcut compared to solving both the momentum and energy cnservation equations for two unknowns. It should give the same reult if I did the math right.