A small motorboat can move at a constant speed of 3.0 m/s relative to the surrounding water. The river in which the boat is traveling flows uniformly toward the east at 2.0 m/s. The river is 150 m wide, with its banks running exactly north–south. Two observers watch the motion: Observer S stands on the north bank, while Observer B rides in the boat.
Respond to the following prompts; answer in complete sentences and include clear reasoning tied to the given information.
(a) State the velocity vector of the boat as measured by Observer B and separately as measured by Observer S. Express each vector in terms of magnitude and cardinal direction (e.g., “north,” “east,” or a combination thereof).
(b) Describe qualitatively why Observer B judges the boat to travel straight across the river, whereas Observer S does not. In your explanation, explicitly refer to the role of each observer’s reference frame.
(c) Identify the reference frame in which the water is at rest and explain how this choice of frame leads to a purely perpendicular path across the river for the boat.
(d) Without performing any calculations, explain whether the crossing time measured by Observer B is the same as, greater than, or less than the time measured by Observer S. Justify your response using appropriate physical reasoning.