Ground Speed of Plane in Windy Conditions

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Homework Help Overview

The problem involves a jet flying due east while experiencing a wind blowing to the northwest, affecting its ground speed. The jet's airspeed is given as 520 km/h, and it is climbing at 100 km/h. Participants are tasked with determining the ground speed of the plane while considering the wind's influence.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the components of velocity in vector form and question the setup of equations regarding the wind and the plane's airspeed. There are attempts to express the velocities in terms of vectors, with some participants noting potential errors in the initial equations presented.

Discussion Status

The discussion is ongoing, with participants providing guidance on the need for vector representation of velocities. There are multiple interpretations being explored regarding the relationships between the wind, the plane's airspeed, and the resulting ground speed.

Contextual Notes

Some participants highlight that the wind is not orthogonal to the plane's airspeed, indicating a need for careful consideration of vector components. There are also mentions of potential errors in the formulation of equations related to the problem.

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Homework Statement


A Jet is heading due east: its nose points towards the east direction, but its trajectory on the ground deviates from the east direction due to a sideways component of the wind. The plane is also climbing at the rate of 100 km/h (height increase per unit time). If the plane's airspeed is 520 km/h and there is a wind blowing 90 km/h to the northwest, what is the ground speed of the plane?

Homework Equations

√x2+y2+z2=a

The Attempt at a Solution

Is y=90j
z=100k

√x2+y2+z2=520 ?

And you solve for x?
 
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NeedHelpBro said:

Homework Statement


A Jet is heading due east: its nose points towards the east direction, but its trajectory on the ground deviates from the east direction due to a sideways component of the wind. The plane is also climbing at the rate of 100 km/h (height increase per unit time). If the plane's airspeed is 520 km/h and there is a wind blowing 90 km/h to the northwest, what is the ground speed of the plane?

Homework Equations

√x2+y2+z2=a

The Attempt at a Solution

Is y=90j
z=100k

√x2+y2+z2=520 ?

And you solve for x?

Try it and see!

BTW: your equations for y and z are wrong: y is a scalar and j is a vector, so you cannot have y = 90j, because a scalar cannot equal a vector. Your z-equation is wrong for the same reason.
 
Not only that, but you should also note that the wind is not orthogonal to the plane’s airspeed velocity. You need to find an expression for the total velocity in vector form.
 
Ray Vickson said:
Try it and see!

BTW: your equations for y and z are wrong: y is a scalar and j is a vector, so you cannot have y = 90j, because a scalar cannot equal a vector. Your z-equation is wrong for the same reason.

Orodruin said:
Not only that, but you should also note that the wind is not orthogonal to the plane’s airspeed velocity. You need to find an expression for the total velocity in vector form.
I have tired my above equation and give me incorrect answer compare to answer provided.

How do find equation of the plane? I have draw what i think the question is asking. Is this correct?

upload_2018-4-1_19-9-47.png
 

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