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What you want to do is first find the momentum of the dog. To find that you will just multiply mass x velocity or in your case 15kg x 4.0 m/s. Once you find that you want to equal the momentum to the momentum of Lillian. Now since Lillian is already at rest, you want to add the masses of both Lillian and the dog together since when she does begin to move, she has a combined mass of both her dog and herself. Then you want to find the missing velocity. So it should look like this:
45kg x v = 60
Now just find v and you should be good:
45kg x v = 60
45v/45 = 60/45 (divide each side by 45 to isolate v)
v = 1.3333333
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