Consider two cases in which cart A moves to the left with momentum p$$i$$and then collides with a second cart which is initially at rest on a horizontal, frictionless air track.

In case $1,$ cart A moves to the left after the collision at a speed of $1$ m$/$s$.$ In case $2,$ cart A moves to the right after the collision with the same speed as in case $1(1$ m$/$s$).$

After the collision, the magnitude of the second cart's momentum in case $1$ is $\_\_\_\_\_\_\_$ the magnitude of the second cart's momentum in case $2.$