On the map, let the +x-axis point east and the +y-axis north.

An airplane flies at 990 km/h northwestward direction (i.e., midway between north and west). Find the components of its velocity.

Repeat for the case when the plane flies due south at the same speed.

hey, you try.

To find the components of the airplane's velocity, we can break it down into its northward and westward components.

For the first case:

Since the airplane is flying northwestward, which is midway between north and west, we can split its velocity into equal parts in each direction.

Let's call the northward component Vy and the westward component Vx.

To find Vy, we can use trigonometry. The northwestward direction forms a right triangle with the northward and westward components as the legs. The angle between the direction and the northward axis is 45 degrees (since it's halfway between north and west).

We can use the sine function to find Vy:
sin(45 degrees) = Vy / 990 km/h

Solving for Vy, we have:
Vy = 990 km/h * sin(45 degrees)

Similarly, we can use the cosine function to find Vx:
cos(45 degrees) = Vx / 990 km/h

Solving for Vx, we have:
Vx = 990 km/h * cos(45 degrees)

Now, let's calculate the values:

Vy = 990 km/h * sin(45 degrees)
Vy ≈ 990 km/h * 0.7071
Vy ≈ 700.44 km/h

Vx = 990 km/h * cos(45 degrees)
Vx ≈ 990 km/h * 0.7071
Vx ≈ 700.44 km/h

Therefore, the components of the airplane's velocity when flying northwestward are approximately Vx = 700.44 km/h (westward) and Vy = 700.44 km/h (northward).

For the second case:

Since the airplane is flying southward, there is no westward velocity component. The entire velocity will be in the southward direction.

Let's call the southward component Vy.

To find Vy, we can use basic trigonometry. The southward direction forms a right triangle with the northward axis as the hypotenuse and Vy as the opposite side.

We can use the sine function to find Vy:
sin(90 degrees) = Vy / 990 km/h

Solving for Vy, we have:
Vy = 990 km/h * sin(90 degrees)

Now, let's calculate the value:

Vy = 990 km/h * sin(90 degrees)
Vy = 990 km/h

Therefore, the component of the airplane's velocity when flying due south is Vy = 990 km/h (southward).