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So basically, it starts out with m[itex]\dot{v}_{y}[/itex]=mg - bv[itex]_{y}[/itex] and you find v[itex]_{ter}[/itex] by letting m[itex]\dot{v}_{y}[/itex]=0 where when you solve for v[itex]_{y}[/itex] you will get v[itex]_{ter}[/itex]. Now the book states how we must now discuss how the projectile approaches that speed and the formula it writes is m[itex]\dot{v}_{y}[/itex] = -b(v[itex]_{y}[/itex] - v[itex]_{ter}[/itex]). Although I get the general idea behind it, can someone explain to me exactly what's going on?

Is this function specific to the 1D case where gravity is the counteracting force to drag?

How was he able to replace v[itex]_{y}[/itex] with v[itex]_{y}[/itex] - v[itex]_{ter}[/itex] and exclude gravity?

Thanks!