Final answer:
The displacement for the cyclist's first trip, after traveling 4 km East and then 7 km West, is -3 km, indicating a final position 3 km West of the starting point.
Step-by-step explanation:
The student is asking about the concept of displacement, which is a vector representing the change in position of a cyclist who moves in one direction, turns around, and moves in the opposite direction. Displacement takes into account the overall change in position and not the distance covered during the journey. In this scenario, the cyclist rides 4 km East and then turns around and rides 7 km West. Since East is considered the positive direction, we can calculate the rider's displacement for her first trip as follows:
- Initial displacement towards the East: +4 km
- Subsequent displacement towards the West: -7 km (because West is the negative direction)
- Total displacement: 4 km - 7 km = -3 km
The negative sign indicates that the final displacement of the cyclist is 3 km to the West from the starting point.