Final answer:
The relationship between the speeds of Alice's horse and Bob's horse varies depending on the direction and magnitude of their movement. In some cases, they move at equal speeds but different directions, while in others, one is faster than the other or they have the same velocity vector.
Step-by-step explanation:
The speed or velocity of Alice's horse and Bob's horse in various scenarios can be compared to determine which horse is moving faster, if they are moving at the same speed, or if the relationship between their speeds cannot be determined without additional context.
- (a) Alice moves north at 6 knots and Bob moves west at 6 knots. They have equal speed but different velocity vectors due to the difference in direction.
- (b) Alice moves west at 6 knots and Bob moves west at 3 knots. Alice's horse is faster (va > ve), as she moves at a higher speed in the same direction.
- (c) Alice moves northeast at 6 knots and Bob moves south at 3 knots. Alice's horse is faster and they have different velocity vectors.
- (d) Alice moves northeast at 6 knots and Bob moves southwest at 6 knots. They have equal speed but opposite velocity vectors.
- (e) Alice moves northeast at 2 knots and Bob moves closer to the shore northeast at 2 knots. They have equal speed and the same velocity vectors, as they are moving in the same direction with the same speed.