Final answer:
To determine Plane B's speed with wind influence, the pilot must adjust their course using the components of velocity vectors and trigonometry. By calculating the angle required to head directly north and the northward speed component, the time to reach a destination can be obtained. Average speed for any journey is calculated by dividing the total distance by the total time taken.
Step-by-step explanation:
Calculating Airplane Speed with Wind Influence
To determine Plane B's speed, we would need similar information as provided for Plane A. However, if we were to follow the given example of a small plane that flies at 200 km/h in still air with a wind blowing directly out of the west at 50 km/h, we can calculate the effective velocity and direction it must maintain to fly directly north across land.
This involves the use of vector addition where the plane's velocity vector is combined with the wind's velocity vector. Using trigonometry, specifically the arctangent function, we can determine the angle at which the pilot must head to counteract the wind and continue flying north. The pilot must fly at an angle θ, where θ = arctan(50/200).
To calculate how long it takes to reach a point 300 km north, we consider the northward component of the plane's velocity, which remains at 200 km/h. Thus, the time required is distance divided by speed, which is 300 km / 200 km/h = 1.5 hours.
Now, regarding the average speed of a train mentioned in a different context, this calculation is straightforward. The average speed is the total distance traveled divided by the total time taken. If a train travels 40 miles one way and then returns back, covering 80 miles in total, and it takes 2 hours for the entire journey, then the average speed is 80 miles / 2 hours = 40 miles per hour.