Your airplane leaves 20 degrees north (linear velocity = 845 nm/h), heading to a point due north at 25 degrees north (linear velocity = 815 nm/h). You set the autopilot for due north and go to sleep. If your flight time is 30 mins, how far off in what direction are you if you take no corrective action?

20 degrees north? Normally it should be north of east, east of north, west of north or north of west.

heading to a point due north at 25 degrees north is sketchy too.

I think maybe the 25 and 20 are latitude and we are talking about Coriolis?

A point on earth is moving faster East at 20N than at 25N

Therefore if you head true north. You will end up Eats of the longitude you started out. (Likewise a parcel of air headed toward a low pressure to the North will end up East of the low in the Northern hemisphere. South motion ends up west. So hurricane is counterclockwise)

That clears it up

Yes it's coriolis I'm talking about. I'm still somewhat confused. Im understanding in what directiion the plane is off but how to I calculate the distance the plane is off?

So the question is really asking how fast a point at 20 N moves east due to earth rotation.

That is about 360*60 = 21600 nautical miles in 24 hours times cos of 20
East speed = 21600*.94 nm /24 hr = 845 nm/hr. WE MAINTAIN THAT EAST SPEED because we are now in the air not touching earth.
That is where that came from.
Now if you used cos 25 I suspect you would come out with the 815 given
Now in half an hour you move 845/2 = 423 miles East
BUT the point you headed for only moved 815/2 = 408 nm East
so we end up
423 - 408 = 15 nm East of our landing field.

Calculate the Coriolis acceleration and see what sideways deviation it makes from the desired path during the flight, when using flat-earth non-rotating coordinates.

Deviation = (1/c)*a_c( t^2
Where a_c is the Coriolis acceleration

You could also do it the way Dr WLS said but the question gave you those two east speeds so you might as well use them.

To determine how far off and in what direction you are if you take no corrective action, we can use the concept of vector addition.

Let's break down the given information:

1. The initial position of the airplane is 20 degrees north.
2. The airplane is heading to a point due north at 25 degrees north (meaning it will end up at a latitude of 25 degrees north).
3. The linear velocity of the airplane is 845 nm/h.
4. The linear velocity of the point due north is 815 nm/h.

Now, let's calculate:

First, convert the flight time of 30 minutes to hours by dividing it by 60: 30 minutes ÷ 60 = 0.5 hours.

Next, calculate the distance traveled by the airplane during this time: distance = velocity × time. Therefore:
Distance traveled by the airplane = 845 nm/h × 0.5 h = 422.5 nm.

Since the airplane is heading due north, its latitude will not change during the flight. So, the latitude of the airplane's final position will also be 25 degrees north.

Now, we need to calculate the longitude difference between the starting and final positions.

To do this, we will use the formula for calculating the difference in longitude along a constant latitude line:
Longitude difference = (distance traveled / (radius of the Earth × cos(latitude)).

The radius of the Earth is approximately 3,963.19 nm.

Longitude difference = (422.5 nm / (3,963.19 nm × cos(20 degrees)) = (422.5 / (3,963.19 × 0.9397)) = 0.113.

Therefore, the airplane will drift approximately 0.113 degrees to the east (assuming positive values represent eastward movement) from its original course.

To determine the direction in which the airplane is off course, we need to calculate the bearing angle from the starting point to the final position.

We can use the formula for calculating the bearing angle between two points given their longitudes and latitudes:
Bearing angle = atan2(sin(longitude difference) × cos(final latitude), cos(initial latitude) × sin(final latitude) - sin(initial latitude) × cos(final latitude) × cos(longitude difference)).

Bearing angle = atan2(sin(0.113) × cos(25 degrees), cos(20 degrees) × sin(25 degrees) - sin(20 degrees) × cos(25 degrees) × cos(0.113)).

After evaluating this expression, we find that the bearing angle is approximately 1.4 degrees to the east (assuming positive values represent eastward movement).

Therefore, if you take no corrective action, you will end up approximately 0.113 degrees to the east and have a bearing approximately 1.4 degrees to the east from your desired due north course.