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°

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles

answer: ay  

fonsi  

dy  

oh

oh no, oh no

oh yeah

diridiri, dirididi daddy  

go

sí, sabes que ya llevo un rato mirándote  

tengo que bailar contigo hoy (dy)  

vi que tu mirada ya estaba llamándome  

muéstrame el camino que yo voy (oh)

tú, tú eres el imán y yo soy el metal  

me voy acercando y voy armando el plan  

solo con pensarlo se acelera el pulso (oh yeah)

ya, ya me está gustando más de lo normal  

todos mis sentidos van pidiendo más  

esto hay que tomarlo sin ningún apuro

despacito  

quiero respirar tu cuello despacito  

deja que te diga cosas al oído  

para que te acuerdes si no estás conmigo

despacito  

quiero desnudarte a besos despacito  

firmo en las paredes de tu laberinto  

y hacer de tu cuerpo todo un manuscrito (sube, sube, sube)

(sube, sube)