Final answer:
The average velocity of an airplane returning to its starting point after a trip is 0 km/h because the displacement is zero, despite the speed being constant during the trip.
Step-by-step explanation:
The student's question pertains to the concepts of displacement, velocity, and speed in physics. An airplane flies 1000 kilometers west, then 1000 kilometers north, forming a right-angled triangle with its starting point, and then returns to the starting place by the shortest route, which is the hypotenuse of the triangle. To find the average velocity, we need to calculate the displacement, which refers to the direct straight-line distance from the initial to the final position of the object regardless of the path taken.
Using the Pythagorean theorem, the displacement (d) is:
d = √(1000 km)² + (1000 km)²
d = √(1000000 km² + 1000000 km²)
d = √2000000 km²
d = 1414.21 km
The plane flies this distance directly back to the starting point. Since velocity is a vector quantity, it involves both magnitude and direction. The average velocity is calculated by dividing the displacement by the total time taken for the trip.
Since the aeroplane's speed is 400 km/h, we can calculate the total time (t) for each leg of the journey:
t = (1000 km + 1000 km + 1414.21 km) / 400 km/h
t = 3.5355 h
The average velocity (v) is therefore:
v = displacement / total time
v = 1414.21 km / 3.5355 h
v = 400 km/h
However, since the aeroplane returns to the starting point, the overall displacement for the entire trip is 0. Thus, the average velocity over the entire trip is:
0 km/h
This indicates that there was no change in position from the starting point over the entire duration of the trip, so the answer is option (b) 0 km/h.