Problem 7 English Version

 
A. Two carts are free to move on a frictionless surface.  Cart A has an initial velocity vo and mass mA.  The second cart with mass mB is initially at rest.  Cart A makes a perfectly elastic collision with cart B along their line of centers.  Find the ratio of the masses that makes the kinetic energy transferred to cart B a maximum.

B. If the ratio of the masses is not that calculated above, show that the amount of energy transferred can be increased by inserting a third cart between the first two.   For optimal transfer, the mass of the third particle is the geometric mean of the other two.