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Question is below please answer asap (this is a conservation of momentum problem that I'm struggling with)

A large platform is initially at rest on a smooth frictionless surface. A dog on the platform starts running toward the east. The mass of the dog is one-half the mass of the platform. When the dog moves toward the east with a speed vo, the platform moves toward the ________ with a speed ________.</div possible answers include east ... vo/2, east ... 2 vo, west ... vo/2, west ... 2 vo, none of these


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1 Answer

m = mass of platform
m/2 = mass of dog
Initial total linear momentum is zero.  Final total linear momentum p must also be zero.
p = momentum of dog + momentum of moving platform
u = velocity of moving platform
I am assuming v0 is the speed of the dog relative to the fixed ground.
p = (m/2)v0 + mu = 0 ⇒ u = -v0/2
Since u is opposite to the direction of v0 (the minus sign), the platform moves at speed v0/2 toward the west, relative to the ground.