Consider an airplane that normally has an air speed of 120 km/h in a 105 km/h crosswind blowing from west to east. Calculate its ground velocity when its nose is pointed north in the crosswind?

Add the two perpendicular velocity vectors

V = sqrt[(105)^2 + (120)^2] = 159.5 km/h (ground speed magnitude)

The direction is arctan(105/120) = 41.2 degrees E of N

PLane flying at 220 mph heading north with 20 mph crosswind . What is the heading angle you should take,AND WHAT IS ITS RELATIVE GROUND SPEED.

To calculate the ground velocity of the airplane when its nose is pointed north in a crosswind, we can use vector addition.

Let's break down the velocities involved:

Air speed of the airplane (in calm conditions) = 120 km/h

Crosswind velocity = 105 km/h (blowing from west to east)

Now, let's refer to the directions:

North = Up

East = Right

West = Left

Since the nose of the airplane is pointing north, we are only concerned with the northward component of the crosswind's velocity. The eastward component of the crosswind will have no effect on the airplane's northward movement.

To calculate the ground velocity, we need to find the resultant vector that combines the air speed and the northward component of the crosswind velocity.

Using Pythagoras' theorem, we can determine the magnitude (speed) of the resultant vector:

Resultant speed = √(Air speed² + Northward component²)
Resultant speed = √(120² + 105²)
Resultant speed = √(14400 + 11025)
Resultant speed = √25425
Resultant speed ≈ 159.43 km/h

Therefore, the ground velocity of the airplane, when its nose is pointed north in the crosswind, is approximately 159.43 km/h.

To calculate the ground velocity of the airplane when its nose is pointed north in a crosswind, we need to use vector addition.

Here's a step-by-step breakdown:

1. Start by drawing a diagram illustrating the situation. Draw a horizontal line to represent the direction of the crosswind from west to east and label it as "crosswind velocity" with a value of 105 km/h. Then, draw a vertical line perpendicular to the crosswind line to represent the direction of the airplane's nose when pointing north.

2. Now, break down the velocity vectors into their horizontal and vertical components. The crosswind velocity can be broken into its horizontal component (eastward) and the vertical component (zero since the wind is not blowing up or down). The airplane's airspeed can be broken into its horizontal component (zero since it is perpendicular to the crosswind) and the vertical component (northward).

3. Calculate the horizontal component of the ground velocity by adding the horizontal components of the crosswind velocity and airspeed. Since the airplane's horizontal airspeed component is zero, the horizontal ground velocity component will be equal to the crosswind's horizontal component, which is 105 km/h.

4. For the vertical component of the ground velocity, add the vertical components of the crosswind velocity and airspeed. The crosswind's vertical component is zero, and the vertical component of the airplane's airspeed is its full value (120 km/h) since it is pointing directly north.

5. Using the Pythagorean theorem, we can calculate the magnitude of the ground velocity vector. Let's call it Vg. The magnitude of Vg is given by √((horizontal component)^2 + (vertical component)^2). In this case, it would be √((105 km/h)^2 + (120 km/h)^2).

6. Calculate the magnitude of Vg: √(11,025 km^2/h^2 + 14,400 km^2/h^2) ≈ √25,425 km^2/h^2 ≈ 159.47 km/h.

7. Finally, determine the direction of the ground velocity. Since the vertical component (northward) is larger than the horizontal component (eastward), the ground velocity is inclined towards the north. Therefore, we can say that the ground velocity of the airplane, when its nose is pointed north in the crosswind, is approximately 159.47 km/h, inclined towards the north.

Note: These calculations assume ideal conditions and ignore other factors that can influence the airplane's velocity, such as air resistance or variations in wind speed at different altitudes.