Ground Speed of Plane in Windy Conditions

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SUMMARY

The discussion focuses on calculating the ground speed of a jet flying due east while climbing at 100 km/h, with an airspeed of 520 km/h and a northwest wind of 90 km/h. The correct approach involves using vector components to account for the wind's influence on the plane's trajectory. Participants emphasize the need to express the total velocity in vector form and correct misconceptions regarding scalar and vector relationships in the equations presented. The final ground speed calculation requires resolving the wind's vector components and applying the Pythagorean theorem.

PREREQUISITES
  • Understanding of vector components in physics
  • Familiarity with the Pythagorean theorem
  • Knowledge of airspeed and ground speed concepts
  • Basic principles of vector addition and subtraction
NEXT STEPS
  • Learn how to resolve vectors into components using trigonometric functions
  • Study the concept of relative velocity in fluid dynamics
  • Explore the application of the Pythagorean theorem in three-dimensional space
  • Investigate the effects of wind on aircraft performance and navigation
USEFUL FOR

Aerospace engineers, physics students, pilots, and anyone interested in understanding the impact of wind on aircraft ground speed calculations.

NeedHelpBro
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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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