A mouse of mass 5.0 g spots the corner of a peanut butter sandwich of mass 8.0 g left on an ice rink after a game. Excited, the mouse runs out onto the ice, but immediately begins to slide. The mouse reaches the peanut butter sandwich and sinks its teeth in. Both the mouse and peanut butter sandwich continue to slide with a speed of 0.45 m/s. What was the initial speed of the mouse?

Answer 1

They want you to neglect friction.
Total momentum is conserved, and equals the initial mouse momentum.

0.005*V0 = (0.005 + 0.008)*0.45
Vo = 13/5 * 0.45 = 1.17 m/s

Answer 2

1.17 m/s