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

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

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Relative Velocity

It is a measurement of an object with regards to the other object which is moving or stable or stationary. For example, if we are traveling in a bus and the bus is moving at speed of 50km/hr, then our speed is according to the nearby passenger on the bus is zero. According to them, we are not moving. But if one person standing on the ground or road observes us from outside of the bus, according to him we are moving at a speed of 50km/hr and the bus is also moving at a speed of 50km/hr. Now, the motion is recognized by the observer, it depends on a frame of reference or observer. This is motion called relative motion.

Question

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

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