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

A)An airplane flies at 990 km/h northwestward direction (i.e., midway between north and west). Find the components of its velocity.
B)Repeat for the case when the plane flies due south at the same speed.

To find the average velocity component to the east, for example, you need to find the distance traveled to the east, and divide by the TOTAL time. To find the average speed, you need to add the distance traveled to the east, and the distance traveled to the north, and divide by the total time.

north 990 sin 45 = y component

west 990 cos 45 = NEGATIVE x component

south is -990 y component
and zero x component

A) To find the components of the velocity when the airplane flies northwestward, we need to break down the velocity into its eastward and northward components.

The northwestward direction is midway between north and west. This means that the angle between the velocity vector and the positive x-axis is 45 degrees.

To find the eastward component of the velocity, we can use trigonometry. We can use the cosine of the angle (45 degrees) to determine the ratio of the eastward component to the total velocity. Since the velocity is given as 990 km/h, the eastward component can be calculated as:

Eastward component = 990 km/h * cos(45°)

Similarly, to find the northward component of the velocity, we use the sine of the angle (45 degrees) to determine the ratio of the northward component to the total velocity. The northward component can be calculated as:

Northward component = 990 km/h * sin(45°)

B) When the plane flies due south at the same speed (990 km/h), the direction becomes straight down the negative y-axis.

To find the eastward component of the velocity in this case, we can use the same trigonometric approach as before. But since the plane is flying due south, the angle between the velocity vector and the positive x-axis is now 90 degrees. So the eastward component will be:

Eastward component = 990 km/h * cos(90°)

Since cos(90°) equals 0, the eastward component will be zero.

To find the northward component of the velocity when the plane flies due south, we need to consider that it is moving in the negative y-axis direction. So the northward component will be:

Northward component = 990 km/h * (-1)

Since the plane is moving in the negative y-axis direction, the northward component will be negative.

Remember, average velocity components are found by dividing the distance traveled in a specific direction by the total time taken. And average speed is found by dividing the total distance traveled (combining both eastward and northward distances) by the total time taken.