Judy (mass 40kg) standing on slippery ice, catches her dog atti(mass 15kg) leaping toward her at 3.0 m/s. use conservation of momentum to show that the speed of judy and her dog after the catch is 0.8 m/s .

Conservation of momentum => momentum before catch = momentum after catch.

Momentum before catch:
 Judy's mass * Judy's velocity +  dog's mass * dog's velocity = 40 kg * 0m/s + 15 kg * 3.0 m/s = 0 + 45.0 kg * m/s

Momentum after catch:

Mass of Judy and dog * velocity = (40 kg + 15 kg)*v = 55kg*v

Equaility of the momenta:

55kg*v = 45.0 kg * m/s

Divide both sides by 55 kg

v = [45.0 / 55] m/s = 0.82 m/s

Using one significative figure: v =  0.8 m/s