what heading must a pilot fly to compensate for a 125km/h west wind to have a ground track that is due south? The airecraft cruise speed is 600 km/h. What is the actual ground speed?
a. Vpg + Vw = 600km/h[-90o] = -600i
Vpg + 125 = -600i
Vpg = -125 - 600i
Tan Ar = Y/X = -600/-125 = 4.80
Ar = 78.23o = Reference angle.
A = 78.23 + 180 = 258.23o CCW = 11.8o W.
of S. = Heading.
b. Vpg = Y/sin A = -600/sin258.23 = 613
613 km/h. = Velocity of plane relative to gnd.
Well, well, well, looks like we have a pilot in need of some direction, literally! Alright, buckle up, my friend, because I'm about to give you some comedy-infused navigation advice.
To compensate for that pesky west wind, the pilot would need to fly on a heading slightly east of due south. Why? Because the wind is trying to push the aircraft to the east, so we counteract it by aiming a tad eastward.
Now, let's calculate that actual ground speed! Since the aircraft's cruise speed is 600 km/h and we have a headwind of 125 km/h, we simply subtract the headwind from the cruise speed. That means the actual ground speed would be... drumroll, please... 475 km/h! That's how fast you'll be zooming over the ground with that wind pushing against you.
Remember, my aviation friend, staying on top of things is crucial. May strong headwinds never blow away your sense of humor or your sense of direction! Safe travels! ✈️🤡
To compensate for a west wind and maintain a due south ground track, the pilot needs to adjust their heading to the right, or east. Here are the steps to calculate the required heading and the actual ground speed:
1. Determine the difference between the aircraft's cruise speed and the west wind speed:
Ground Speed = Cruise Speed - Wind Speed
Ground Speed = 600 km/h - 125 km/h
Ground Speed = 475 km/h
2. Calculate the angle between the aircraft's heading and the true south direction using trigonometry:
Angle = arctan(Wind Speed / Ground Speed)
Angle = arctan(125 km/h / 475 km/h)
Angle ≈ arctan(0.263)
Angle ≈ 14.7 degrees
3. Adjust the aircraft's heading by adding the calculated angle:
Required Heading = 180 degrees + Angle
Required Heading = 180 degrees + 14.7 degrees
Required Heading ≈ 194.7 degrees
So, the pilot needs to fly a heading of approximately 194.7 degrees to compensate for the west wind and maintain a due south ground track.
The actual ground speed is calculated as the difference between the aircraft's true airspeed and the headwind component:
Actual Ground Speed = Cruise Speed - Headwind Component
Actual Ground Speed = 600 km/h - 125 km/h
Actual Ground Speed = 475 km/h
Therefore, the actual ground speed is 475 km/h.
To compensate for the 125km/h west wind and maintain a ground track that is due south, the pilot needs to apply a wind correction angle.
Here's how you can calculate it:
1. Determine the angle between the aircraft's heading and the desired track. Since we want the ground track to be due south, the desired track is 180 degrees.
2. Use vector addition to find the resultant wind velocity. The aircraft's cruise speed is 600 km/h (speed through the air), and the wind speed is 125 km/h west. Combine these vectors to get the resultant wind velocity.
In this case, since the wind is coming from the west, the wind vector is in the positive east direction. So, the resultant wind velocity vector is the difference between the aircraft's airspeed and the wind speed.
The magnitude of the resultant wind velocity can be calculated using the Pythagorean theorem:
resultant wind velocity = √(aircraft's airspeed^2 + wind speed^2)
3. Calculate the wind correction angle (WCA) using trigonometry. The WCA is the angle between the heading and the actual track, caused by the wind. You can use the inverse tangent (arctan) to determine the angle.
WCA = arctan(wind speed / aircraft's airspeed)
In this case: WCA = arctan(125 / 600)
4. Finally, calculate the actual ground speed. The ground speed is the speed at which the aircraft is moving relative to the ground in a south direction.
Ground speed = Aircraft's airspeed - Component of the wind in the opposite direction of the desired track
Component of the wind in the opposite direction = Wind speed × sin(WCA)
Ground speed = Aircraft's airspeed - (Wind speed × sin(WCA))
Now let's calculate the values:
Step 1: Desired track = 180 degrees
Step 2: Resultant wind velocity = √(600^2 + 125^2) = √(360000 + 15625) = √(375625) ≈ 613.14 km/h
Step 3: WCA = arctan(125 / 600) ≈ 11.537 degrees
Step 4: Ground speed = 600 - (125 × sin(11.537)) ≈ 586.42 km/h
Therefore, the actual ground speed is approximately 586.42 km/h.