Final answer:
Maryam has an average speed of 54 km/h for her entire journey, whereas the magnitude of her average velocity is approximately 38.44 km/h, calculated based on the straight-line displacement over the total trip time.
Step-by-step explanation:
Maryam's driving journey consists of two separate trips. First, she drives 120 km due south at a speed of 60 km/h, and then she drives 150 km due east at a speed of 50 km/h. To calculate the average speed for the entire journey, we need to find the total distance and the total time of the trip.
The time taken to travel 120 km at 60 km/h is 120 km / 60 km/h = 2 hours. The time taken to travel 150 km at 50 km/h is 150 km / 50 km/h = 3 hours. The total time for the trip is 2 hours + 3 hours = 5 hours, and the total distance is 120 km + 150 km = 270 km.
The average speed for the trip is then calculated as the total distance divided by the total time, which is 270 km / 5 h = 54 km/h.
For part b, the magnitude of the average velocity is determined by finding the straight-line distance between the start and end points (displacement) and dividing it by the total time. Since the trip is a right-angled triangle (120 km south and 150 km east), we use the Pythagorean theorem to find the displacement: √(120² + 150²) km = √(14400 + 22500) km = √(36900) km ≈ 192.2 km.
Thus, the magnitude of the average velocity is 192.2 km / 5 h ≈ 38.44 km/h.