A woman is on a train leaving the station at \(4.0 \mathrm{~m} / \mathrm{s}\), while a friend waving goodbye runs alongside the car she's in.

(a) If the friend is running at \(6.0 \mathrm{~m} / \mathrm{s}\) and moving in the same direction as the train, how fast must the woman walk, and in which direction, to keep up with him?

(b) Once the train has reached a speed of \(10 \mathrm{~m} / \mathrm{s}\), how fast must the woman walk, and in which direction, to keep up with her friend?