A plane is flying to a city 716 km directly north of its initial location. Therefore the only component of the planes velocity relative to the earth most always be north The plane maintains a speed of 203 km/h relative to the air during its flight. The air is not standing still but has speed of 51.5 km/h relative to the earth. .(Let the +x-axis point East and the and the +y-axis point North) Let p=Plane, a =Air. e=Earth Using double subscript notation and write the vector components for the velocity of the Plane relative to the Earth (1) Vpex = (2) Vpey = From the given the velocity of the plane relative to ground always has a "x-component" (east-west direction) of (3) Vpex = From the given the magnitude of the velocity of the plane relative to the air always is km (4) |Vpa| = hr From the given the magnitude of the velocity of the air relative to the air always is km (5) |Vael = hr Therefore , from equation (1) and (3) the angle the plane must fly at relative to the air direction can be found from

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A plane is flying to a city 716 km directly north of its initial location. Therefore the only component of the
planes velocity relative to the earth most always be north The plane maintains a speed of 203 km/h relative
to the air during its flight. The air is not standing still but has speed of 51.5 km/h relative to the earth. .(Let
the +x-axis point East and the and the +y-axis point North) Let p=Plane, a =Air. e=Earth
Using double subscript notation and write the vector components for the velocity of the Plane relative to the
Earth
(1) Vpex =
(2) Vpey =
+
From the given the velocity of the plane relative to ground always has a "x-component" (east-west direction)
of
(3) Vpex =
From the given the magnitude of the velocity of the plane relative to the air always is
km
(4) |Vpa| =
hr
From the given the magnitude of the velocity of the air relative to the air always is
km
(5) |Vae =
hr
Therefore , from equation (1) and (3) the angle the plane must fly at relative to the air direction can be found
from
(6) cos(v)
|Vacz|
Vpa
Transcribed Image Text:A plane is flying to a city 716 km directly north of its initial location. Therefore the only component of the planes velocity relative to the earth most always be north The plane maintains a speed of 203 km/h relative to the air during its flight. The air is not standing still but has speed of 51.5 km/h relative to the earth. .(Let the +x-axis point East and the and the +y-axis point North) Let p=Plane, a =Air. e=Earth Using double subscript notation and write the vector components for the velocity of the Plane relative to the Earth (1) Vpex = (2) Vpey = + From the given the velocity of the plane relative to ground always has a "x-component" (east-west direction) of (3) Vpex = From the given the magnitude of the velocity of the plane relative to the air always is km (4) |Vpa| = hr From the given the magnitude of the velocity of the air relative to the air always is km (5) |Vae = hr Therefore , from equation (1) and (3) the angle the plane must fly at relative to the air direction can be found from (6) cos(v) |Vacz| Vpa
If the plane flies through a constant headwind blowing south at 51.5 km/h, find the speed of the plane relative
to the earth and how much time (in h) will it take to reach the city?
From the given we have
Vaex =
km
hr
km
Vaey =
hr
Substituting into our double subscript notation equations above we can solve for the speed of the plane
relative to the earth
km
Vpey =
hr
The time of travel for the trip is
ttrip
hr
Transcribed Image Text:If the plane flies through a constant headwind blowing south at 51.5 km/h, find the speed of the plane relative to the earth and how much time (in h) will it take to reach the city? From the given we have Vaex = km hr km Vaey = hr Substituting into our double subscript notation equations above we can solve for the speed of the plane relative to the earth km Vpey = hr The time of travel for the trip is ttrip hr
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