(wr2)a = (Vr)a = [Vr + (Vr)e] = constant (1)
Note that w is positive if rotation is counterclockwise relative to North Pole. Thus, V is positive if the zonal motion vector is oriented west to east.
[Vr + (Vr)e]f = [Vr + (Vr)e]i (2)
Solve for Vf, the tangential velocity relative to the earth at the final latitude.
Vf = [Vr + (Vr)e]f – [(Vr)e]f (3)
r = radial distance to axis of rotation = R cos ¿ (4)
Ve =WRcos ¿ (5)
Substitute (5) into (3) and simplify by inserting initial Vi = 0
Vf = 482.7 km s-1