An airplane is traveling in the direction 20degrees west of north at 700 km/hr. Find the component form of velocity of the airplane assuming that the positive x-axis represents due east and the positive y-axis represents due north.

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To find the component form of the velocity of the airplane, we need to break down the given velocity into its north and east components.

Given:
Direction = 20 degrees west of north
Velocity magnitude = 700 km/hr

Step 1: Define the coordinate system
The positive x-axis represents due east, and the positive y-axis represents due north.

Step 2: Break down the velocity into components
Since the airplane is traveling in the direction 20 degrees west of north, we need to find the north and east components.

The north component can be calculated using the sine function:
North component = Velocity magnitude * sin(angle)

The east component can be calculated using the cosine function:
East component = Velocity magnitude * cos(angle)

Step 3: Calculate the components
North component = 700 km/hr * sin(20 degrees)
East component = 700 km/hr * cos(20 degrees)

Step 4: Convert into component form
The component form of velocity can be written as a vector <Vx, Vy>, where Vx represents the east component, and Vy represents the north component.

Therefore, the component form of the velocity of the airplane is:
<Vx, Vy> = <700 km/hr * cos(20 degrees), 700 km/hr * sin(20 degrees)>

Note that the velocity components can be rounded to an appropriate number of decimal places based on the desired level of accuracy.

To find the component form of velocity, we need to break down the velocity vector into its x and y components.

Given that the positive x-axis represents due east and the positive y-axis represents due north, we can use basic trigonometry to solve this problem.

Let's consider the given information:
- The airplane is traveling at a speed of 700 km/hr.
- The airplane is traveling in the direction 20 degrees west of north.

To find the x-component of velocity, we need to determine the component of velocity in the east-west direction. Since the positive x-axis represents due east, any direction west of north can be considered as negative along the x-axis. Therefore, the x-component will be negative.

To find the y-component of velocity, we need to determine the component of velocity in the north-south direction. Since the positive y-axis represents due north, the y-component will be positive.

Now, we can determine the components of velocity using trigonometry.

The x-component, Vx, can be calculated using the formula:
Vx = V * cos(theta)

where V is the velocity magnitude (700 km/hr) and theta is the angle between the velocity vector and the positive x-axis. In this case, since the airplane is traveling 20 degrees west of north, the angle theta is 70 degrees.

Substituting the values, we get:
Vx = 700 km/hr * cos(70°)

The y-component, Vy, can be calculated using the formula:
Vy = V * sin(theta)

Substituting the values, we get:
Vy = 700 km/hr * sin(70°)

Thus, the component form of the velocity vector is:
V = (-700 km/hr * cos(70°))i + (700 km/hr * sin(70°))j

where i represents the x-direction (east-west) and j represents the y-direction (north-south).

Vx = -700 sin20 = -239.4 km/h

Vy = 700 cos20 = +657.8 km/h