I only need the speed and direction of the wind.
An airplane has an airspeed of 300 mph, and it is traveling to the southwest. After two hours it is 282.9 miles from its starting point, at a compass heading of 228.6° from the starting point.
To determine the speed and direction of the wind, we need to analyze the airplane's groundspeed and the difference between its airspeed and groundspeed.
Here's how you can calculate it:
1. Determine the groundspeed:
Groundspeed is the speed at which the airplane actually moves over the ground, taking into account both its airspeed and the effect of any wind. In this case, the airplane's groundspeed can be calculated by dividing the distance covered by the time taken:
Groundspeed = Distance / Time
Groundspeed = 282.9 miles / 2 hours
Groundspeed = 141.45 mph
2. Determine the speed and direction of the wind:
To find the speed of the wind, we subtract the airplane's airspeed from its groundspeed:
Wind speed = Groundspeed - Airspeed
Wind speed = 141.45 mph - 300 mph
Wind speed = -158.55 mph
The negative sign indicates that the wind is blowing opposite to the airplane's direction.
To find the direction of the wind, we need to determine the angle between the airplane's track (heading) and its actual ground track. This is known as the crab angle.
Crab angle = 228.6° - 225° (southwest heading)
Crab angle = 3.6°
So, the direction of the wind can be determined by adding the crab angle to the airplane's track (heading):
Wind direction = Airplane's track + Crab angle
Wind direction = 225° + 3.6°
Wind direction = 228.6°
Therefore, the speed of the wind is 158.55 mph (blowing opposite to the airplane's direction) and the wind is coming from a compass heading of 228.6°.