A small airplane has an air speed of The pilot wishes to fly to a destination that is 480 km due west from the plane’s present location. There
is a wind from the south.
To determine the actual ground speed and heading the pilot needs to achieve in order to reach the destination, we need to consider the effects of the wind.
Given that the wind is coming from the south, it will affect the airplane's movement. We will need to calculate the wind's impact on both the aircraft's airspeed (actual speed of the airplane through the air) and its course or heading (direction the airplane must point in order to fly directly to the destination).
Here's how we can calculate it step by step:
1. Determine the wind's speed and direction. Let's assume the wind speed is W km/h and it's blowing from the south (upwards on a map).
2. Determine the aircraft's airspeed. The question doesn't provide the airspeed, so let's assume it is A km/h.
3. Calculate the ground speed. The ground speed is the speed of the aircraft relative to the ground. It can be determined by subtracting the wind's speed from the aircraft's airspeed:
Ground Speed = Airspeed - Wind Speed
G = A - W
4. Calculate the course or heading. Since the destination is to the west, the aircraft needs to adjust its heading to compensate for the wind pushing it to the north. Let's assume the aircraft's original heading (without wind correction) for simplicity is due west (270 degrees on a compass). The wind's direction is from the south (180 degrees on a compass). To correct, we need to subtract the wind's direction from the desired heading:
Course = Desired Heading - Wind's Direction
C = 270 - 180
The resulting course would be the heading the pilot should aim for to counteract the wind's effect.
By using these calculations, the pilot can determine the necessary ground speed and heading to reach the destination. However, it's important to note that these calculations may vary depending on the specific situation and the actual values of airspeed and wind speed provided.