Relative velocity

[rachelmaddie]

Hi. I need my work checked please.

6)
Component of the plane’s velocity in the direction of vector j point north relative to the air: 173cos18°

Component of the plane’s velocity in the direction of vector k point up relative to the air: 173sin18°

The direction of the plane’s velocity relative to the air is normal to vector i point east. Therefore, the component of the plane’s velocity (relative to the air) in that direction will be equal to zero.
Thus, velocity of plane relative to air = 0 vector i point east + (173cos18°) vector j point north + (173sin18°) + vector k point up

Component of the velocity of wind in the direction of vector i point up:
42sin47°

Component of the velocity of wind in the direction of vector j point point north:
-42cos47°

Assuming that the wind blows horizontally, the direction of the wind will be normal to vector k point up.
So the component of the velocity of the wind in the direction vector k point up will be equal to zero.
Therefore,
Vwind = (42sin47°) vector i point east + (42cos47°) vector j point north + 0 vector k point up

The ground speed of the plane
Velocity of plane relative to the ground is the sum of Velocity of plane relative to the air and Vwind

Velocity of plane relative to the ground = Vvelocity of plane relative to the air + Vwind


Vplane = 30.72 i point east + 193.18 j point north + 53.46 k point up

 

[HallsofIvy]

Hi. I need my work checked please.
View attachment 21109
6)
Component of the plane’s velocity in the direction of vector j point north relative to the air: 173cos18°

Component of the plane’s velocity in the direction of vector k point up relative to the air: 173sin18°

The direction of the plane’s velocity relative to the air is normal to vector i point east. Therefore, the component of the plane’s velocity (relative to the air) in that direction will be equal to zero.
Thus, velocity of plane relative to air = 0 vector i point east + (173cos18°) vector j point north + (173sin18°) + vector k point up

Since it has already been said that "vector i points east", etc. It is not necessary to repeat that. Also the "+" between "(173sin18°)" and "vector k point up" is wrong- I presume it is a typo. The airplanes velocity vector, relative to the air (it's "airspeed") is 173 cos(18°)j+ 173 sin(18°)k.

Component of the velocity of wind in the direction of vector i point up:

No, i does not "point up" it points north! i presume that was another typo.

42sin47°

Component of the velocity of wind in the direction of vector j point point north:
-42cos47°

The direction of the wind is given as "S47°E". In a 360 degree circle, that would be 180- 47= 133°. The east west component of wind speed would be 42 cos(133°). That is the same as -42 cos(47°). The east west component is 42 sin(133°)= 42 sin(47°). You have the i and j components reversed!

Assuming that the wind blows horizontally, the direction of the wind will be normal to vector k point up.
So the component of the velocity of the wind in the direction vector k point up will be equal to zero.
Therefore,
Vwind = (42sin47°) vector i point east + (42cos47°) vector j point north + 0 vector k point up

Vwind= 42 sin(47°) i- 42 cos(47°)j

The ground speed of the plane
Velocity of plane relative to the ground is the sum of Velocity of plane relative to the air and Vwind

Velocity of plane relative to the ground = Vvelocity of plane relative to the air + Vwind


Vplane = 30.72 i point east + 193.18 j point north + 53.46 k point up

Assuming "Vplane" is the "Velocity of the plane relative to the ground" (you did not actually say that) then
Vplane= 42 sin(47°) i+(173 cos(18°)- 42 cos(47°)) j+ 173 sin(18°)k.

 

[rachelmaddie]

Since it has already been said that "vector i points east", etc. It is not necessary to repeat that. Also the "+" between "(173sin18°)" and "vector k point up" is wrong- I presume it is a typo. The airplanes velocity vector, relative to the air (it's "airspeed") is 173 cos(18°)j+ 173 sin(18°)k.


No, i does not "point up" it points north! i presume that was another typo.


The direction of the wind is given as "S47°E". In a 360 degree circle, that would be 180- 47= 133°. The east west component of wind speed would be 42 cos(133°). That is the same as -42 cos(47°). The east west component is 42 sin(133°)= 42 sin(47°). You have the i and j components reversed!


Vwind= 42 sin(47°) i- 42 cos(47°)j


Assuming "Vplane" is the "Velocity of the plane relative to the ground" (you did not actually say that) then
Vplane= 42 sin(47°) i+(173 cos(18°)- 42 cos(47°)) j+ 173 sin(18°)k.

Is this better??

6)
Component of the plane’s velocity in the direction of vector j point north relative to the air: 173cos18°

Component of the plane’s velocity in the direction of vector k point up relative to the air: 173sin18°

The direction of the plane’s velocity relative to the air is normal to vector i point east. Therefore, the component of the plane’s velocity (relative to the air) in that direction will be equal to zero.
Thus, the airplanes velocity vector, relative to the air (it's "airspeed") is 173 cos(18°)j+ 173 sin(18°)k.


The direction of the wind is given as "S47°E". In a 360 degree circle, that would be 180- 47= 133°. The east west component of wind speed would be 42 cos(133°). That is the same as -42 cos(47°). The east west component is 42 sin(133°)= 42 sin(47°).

Component of the velocity of wind in the direction of vector i points north:
-42cos(47°)

Component of the velocity of wind in the direction of vector j point point north:
42sin(47°)

Assuming that the wind blows horizontally, the direction of the wind will be normal to vector k point up.
So the component of the velocity of the wind in the direction vector k point up will be equal to zero.
Therefore,
Vwind = Vwind= 42 sin(47°) i- 42 cos(47°)j

The ground speed of the plane
Velocity of plane relative to the ground is the sum of Velocity of plane relative to the air and Vwind

Velocity of plane relative to the ground = Vvelocity of plane relative to the air + Vwind

Assuming "Vplane" is the "Velocity of the plane relative to the ground"
Vplane= 42 sin(47°) i+(173 cos(18°)- 42 cos(47°)) j+ 173 sin(18°)k.