Final answer:
The total distance traveled by the airplane is 750 km, and the total displacement is 150 km west. The average velocity of the trip is 80 km/h west, and the average speed is 401.07 km/h.
Step-by-step explanation:
a. To find the total distance traveled by the airplane, you need to sum up the distances traveled in each leg of the journey.
100 km north + 150 km west + 500 km south = 750 km
Therefore, the total distance traveled by the airplane is 750 km.
To find the total displacement of the airplane, you need to consider the net distance and direction of the journey. Since the airplane is moving in different directions, we need to break down the vectors and add them up.
The northward vector cancels out the southward vector because they are in opposite directions. The westward vector remains. Therefore, the displacement of the airplane is 150 km west.
b. Average velocity is the displacement divided by the total time taken.
Displacement = 150 km west
Total time = 20 min (north) + 40 min (west) + 52 min (south) = 112 min = 1.87 hours
Average velocity = 150 km west / 1.87 hours = 80 km/h west
Average speed is the total distance traveled divided by the total time taken.
Total distance = 100 km north + 150 km west + 500 km south = 750 km
Total time = 112 min = 1.87 hours
Average speed = 750 km / 1.87 hours = 401.07 km/h