Mary slides down a snow-covered hill on a large piece of cardboard and then slides across a frozen pond at a constant velocity of +3.0 m/s. After Mary has reached the bottom of the hill and is sliding across the ice, Sue runs after her at a velocity of +

The total momentum of the system before Sue hops on the cardboard is zero since Mary is sliding alone. After Sue hops on, the total momentum is conserved. Therefore, the momentum of the Mary-Sue-cardboard system will be: (mary mass) x (Mary's velocity) + (sue mass) x (Sue's velocity) = Total momentum (68 kg) x (3.0 m/s) + (59 kg) x (4.2 m/s) = total momentum total momentum = 732.2 kg*m/s The total mass of the system is 68 kg + 59 kg = 127 kg. Therefore, the velocity of the Mary-Sue-cardboard system is: (total momentum) / (total mass) = 732.2 kg*m/s / 127 kg = 5.76 m/s Since Sue is hopping on and joining Mary's motion, the direction of their velocity will be the same as Mary's, which is positive (+) in the given problem statement. Therefore, the two of them will slide across the ice together at a speed of 5.76 m/s in the positive direction.