Calculating Average Velocity and Average Speed of the Ship

Given Data:
- Initial velocity in the East direction = 18 km/h
- Velocity after turning south = 9 km/h
- Time spent moving south = 1 hour

Calculating Average Velocity:
- To find the average velocity, we need to consider both the magnitude and direction of the velocities.
- The ship initially moves due East, so its velocity can be represented as 18 km/h East.
- After turning towards the South, the ship has a velocity of 9 km/h South.
- To find the average velocity, we need to find the resultant velocity of the ship. This can be calculated using vector addition.
- The resultant velocity = sqrt((18^2) + (9^2)) = sqrt(405) = 20.12 km/h
- The direction of the resultant velocity can be calculated using trigonometry as atan(9/18) = 26.57 degrees South of East.
- Therefore, the average velocity of the ship is 20.12 km/h 26.57 degrees South of East.

Calculating Average Speed:
- The average speed of an object is defined as the total distance traveled divided by the total time taken.
- The total distance traveled by the ship is the sum of the distances traveled in the East and South directions.
- Distance traveled in the East direction = 18 km/h * t (where t is the total time)
- Distance traveled in the South direction = 9 km/h * 1 hour = 9 km
- Total distance = 18t + 9 km
- Total time = t + 1 hour
- Average speed = Total distance / Total time = (18t + 9) / (t + 1)
- Since the ship traveled for 1 hour in the South direction, the total time is t + 1 hour.
- Therefore, the average speed of the ship is (18t + 9) / (t + 1) km/h.
By following these calculations, we can determine the average velocity and average speed of the ship for the given motion.