a taxi cab drives 2.0 km (W). then 3.0 km (N) , then 4.0 km (W), and finally 5.0 km (N). the entire trip takes 0.30 h. what is the taxi's average velocity?
The total distance travelled by the taxi is 2.0 km + 3.0 km + 4.0 km + 5.0 km = 14.0 km.
The total time taken for the trip is 0.30 hours.
Therefore, the average velocity of the taxi is 14.0 km / 0.30 h = 46.67 km/h (rounded to two decimal places). Answer: \boxed{46.67 \text{ km/h}}.
To find the taxi's average velocity, we need to calculate the total displacement and divide it by the total time.
1. Calculate the total displacement:
- The taxi drives 2.0 km west and then 4.0 km west, so the total displacement in the west direction is 2.0 km + 4.0 km = 6.0 km west.
- The taxi drives 3.0 km north and then 5.0 km north, so the total displacement in the north direction is 3.0 km + 5.0 km = 8.0 km north.
- Combining the displacements in both directions, the total displacement is √((6.0 km)² + (8.0 km)²) = √(36.0 km² + 64.0 km²) = √100.0 km² = 10.0 km.
2. Calculate the total time:
- The entire trip takes 0.30 h.
3. Calculate the average velocity:
- Average velocity = Total displacement / Total time
- Average velocity = 10.0 km / 0.30 h ≈ 33.3 km/h
Therefore, the taxi's average velocity is approximately 33.3 km/h.