A plane flies with a heading of 48 degrees NW and an air speed of 584 km/h. It is driven from its course by a wind of 58.0 km/h from 12.0 degrees SE. Find the ground speed and the drift angle of the plane.

Vp' = Vp + Vw,

Vp'=584km/h @ 138deg + 58km/h @ 348deg.

X = hor. = 584cos138 + 58cos348,
X = hor. = -434 + 56.73 = -377km/h.

Y = ver. = 584sin138 + 58sin348,
Y = ver. = 391 + (-12) = 379km/h.

tanA = Y/X = 379 / -377 = -1.0051.
A = -45deg.,CW.
A = -45 + 360 = 315deg.,CCW.

Vp' = sqrt((-377)^2+(379)^2 = 535km/h = Velocity of plane.

Correction:

A = -45 + 180 = 135deg., CCW. Q2.

Vp' = 535km/h @ 135deg.

To find the ground speed and drift angle of the plane, we can use vector addition.

Let's start by breaking down the given information into vectors:

1. Start with the plane's airspeed of 584 km/h at a heading of 48 degrees NW.

To break this down into components, we can use trigonometry. The NW direction forms a 45-degree angle with both the north and west directions (since NW is halfway between N and W).

The component of the airspeed in the north direction is given by sin(45 degrees) * 584 km/h, which equals approximately 584 * √2/2 km/h.

Similarly, the component of the airspeed in the west direction is given by cos(45 degrees) * 584 km/h, which is also approximately 584 * √2/2 km/h.

So, the plane's airspeed can be represented as a vector (584 * √2/2 km/h, 584 * √2/2 km/h) in the north-west direction.

2. Next, consider the wind of 58.0 km/h from 12.0 degrees SE.

Since the wind is coming from the SE direction, we need to break it down into components in the north and west directions.

The component of the wind in the north direction is given by sin(12 degrees) * 58.0 km/h, approximately 58.0 * sin(12 degrees) km/h.

Similarly, the component of the wind in the west direction is given by cos(12 degrees) * 58.0 km/h, approximately 58.0 * cos(12 degrees) km/h.

So, the wind vector can be represented as (58.0 * cos(12 degrees) km/h, 58.0 * sin(12 degrees) km/h) in the north-west direction.

3. Now, we can find the resultant vector, which represents the actual motion of the plane.

To find the resultant vector, we can add the vectors of the plane's airspeed and the wind together.

The north component of the resultant vector is the sum of the north components of the airspeed and the wind.

Similarly, the west component of the resultant vector is the sum of the west components of the airspeed and the wind.

Hence, the resultant vector can be represented as (584 * √2/2 + 58.0 * cos(12 degrees), 584 * √2/2 + 58.0 * sin(12 degrees)).

4. Finally, we can calculate the ground speed and the drift angle from the resultant vector.

The ground speed of the plane is the magnitude of the resultant vector, given by the square root of the sum of the squares of its components.

Therefore, the ground speed is approximately √[(584 * √2/2 + 58.0 * cos(12 degrees))^2 + (584 * √2/2 + 58.0 * sin(12 degrees))^2] km/h.

The drift angle of the plane is the angle between the direction of the resultant vector and the north direction. This can be calculated using inverse trigonometry.

Hence, the drift angle is given by arctan[(584 * √2/2 + 58.0 * sin(12 degrees)) / (584 * √2/2 + 58.0 * cos(12 degrees))]. We can convert this angle to degrees for convenience.

After calculating the above expressions, you will find the values for the ground speed and drift angle of the plane.