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

Question

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

Answer 1

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.