What are the x-and y-components of an airplane's total velocity with an initial velocity of 200 mph east and an 80 mph wind from north to south?

To determine the x- and y-components of the airplane's total velocity, we need to break down the given velocities into their respective components.

The airplane has an initial velocity of 200 mph traveling east. In terms of components, east corresponds to the positive x-direction. Thus, the x-component of the airplane's velocity is 200 mph. This is represented as ( vx = 200 ) mph.

On the other hand, there is an 80 mph wind blowing from the north to the south. In this case, south corresponds to the negative y-direction. Therefore, the y-component of the wind can be represented as ( vy = -80 ) mph.

When we sum these velocities vectorially, we have:

• The airplane's x-component: ( vx = 200 ) mph (east).

• The wind's y-component: ( vy = -80 ) mph (south).

Thus, the x-and y-components of the total velocity of the airplane can be expressed as ( vx = 200 ) mph and ( vy = -80 ) mph. This results in the correct answer.