19. An aircraft maintaining a constant airspeed of 525 MPH is headed due south. The jet stream is 120 MPH in the northeasterly direction.

a. Sketch the scenario on the x-y axis.

b. Express the velocity of the plane relative to the air as a vector.

c. Express the velocity of the jet stream as a vector.

d. Find the velocity of the plane relative to the ground.

Find the actual speed and direction of the plane relative to the ground. Round to the

tenths.

e.

a. Sketch is given in the attachment

b. = (0,-525)

c. = (,)  

d. = (60, 60  - 525)

e. Actual Speed = || = 448.3 MPH

Direction = Ф = - 79.1°

Direction = Ф = 280.9° with respect to x - axis.

Step-by-step explanation:

a. Sketch the scenario on the x-y axis.

Where,

Velocity of the plane relative to air =

Velocity of the jet stream =

Velocity of the plane relative to ground =

Solution:

Note: Solution is given in the attachment. Please refer to the attachment for the sketch.

b. Express the velocity of the plane relative to the air as a vector.

Solution:

= || cosФi + || sinФj

where,

|| = magnitude of the vector.

|| =  525 MPH

Ф = 270° w.r.t to x - axis. (See the sketch in the attachment)

= || cosФi + || sinФj

Plug in the values into this equation to express it in the vector form as required.

= (525) cos270i + (525) sin270j

As, Cos270 = 0

and

Sin270 = -1

So,

= (525) (0)i + (525) (-1)j

= 0i -525j    

= (0,-525)  

c. Express the velocity of the jet stream as a vector.

Solution:

Velocity of the jet stream as a vector.

= || cosФi + || sinФj

where,

|| = magnitude of the vector.

|| =  120 MPH

Ф = 45°  (See the sketch in the attachment)

= || cosФi + || sinФj

Plug in the values into this equation to express it in the vector form as required.

= (120) cos45i + (120) sin45j

As, Cos45 =

and

Sin45 =  

So,

= (120) ()i + (120) ()j

= 60i +60j    

= (,)  

d. Find the velocity of the plane relative to the ground.

Solution:

Velocity of the plane relative to the ground = Sum of velocity of plane relative to the air and velocity of the jet stream

= +

= 0i -525j    +  60i +60j    

= 60i + 60  - 525j

= (60, 60  - 525)

e. Find the actual speed and direction of the plane relative to the ground. Round to the  tenths.

Solution:

Actual Speed = ||  = magnitude of the velocity of the plane relative to the ground.

Actual Speed = || =

Actual Speed = || = 448.3 MPH

Direction = Ф = ()

Direction = Ф = - 79.1°

To find out the direction with respect to x - axis.

Direction = Ф = 360 - 79.1

Direction = Ф = 280.9°

c

step-by-step explanation:

it would be see because your formula is f(x)=6x, so 6 times 1 is 6 and you go on and the best answer is c.

answer: 4 meters

step-by-step explanation: to you understand 2/3 better you can do 1 divided by 3 = . then multiply that by the 2 which is .66666666666666667 then you would do 6 x .66666666666666667 which is 4.      

hope this .