A plane is heading on a bearing of 200° with an air speed of 400 km/h when it is blown off course by a wind of 100 km/h from the northeast. Determine the resultant ground velocity of the plane. How did you get your answer?

Vr = 400km/h[200o] + 100km/h[225o]

X = 400*Cos200 + 100*Cos225 = -447 km/h
Y = 400*sin200 + 100*sin225 = -208 km/h

Tan Ar = Y/X = -208/-447 = 0.46532
Ar = 25o = Reference angle.
A = 25 + 180 = 205o (Q3).

V = X/Cos A = -447/Cos205 = 493 km/h. =
Resultant velocity.

To determine the resultant ground velocity of the plane, we need to consider both the plane's air speed and the effect of the wind.

Here's how we can calculate it step by step:

1. Start by drawing a vector diagram to visualize the given information. Draw two vectors: one representing the plane's air speed of 400 km/h directed at a bearing of 200°, and another representing the wind of 100 km/h from the northeast.

2. Break down the wind vector into its northward and eastward components. Since the wind is coming from the northeast, it can be split into equal components of 50 km/h each in the northward and eastward directions. This is because the northeast direction is halfway between the northward (0°) and eastward (90°) directions.

3. Add the air speed vector (400 km/h at a bearing of 200°) with the eastward component of the wind (50 km/h directed east).

4. Use vector addition to find the resultant velocity. To do this, add the two vectors obtained in step 3 by considering both their magnitudes (lengths) and directions. The magnitude of the resultant velocity is given by the vector sum of the air speed (400 km/h) and the eastward component of the wind (50 km/h) computed in step 3. The direction can be found by measuring the angle of the resultant vector from a reference direction, usually the north (0°) direction, using compass bearings.

5. Calculate the magnitude and direction of the resultant ground velocity. Substituting the values into the equation, we obtain the magnitude of the resultant ground velocity. The direction will be the bearing of the resultant vector obtained in step 4.

By following these steps, you should be able to determine the resultant ground velocity of the plane.