Finding Velocity of Airplane & Wind: An Analysis of Triangle ABCD

In summary, the problem involves finding the velocity of an airplane and the velocity of wind based on the time and length of its flight over a triangular route. The velocity of the airplane is constant relative to the wind, and the wind itself has a constant velocity. The solution involves setting up equations using known values for the sides of the triangle and using the fact that the velocity of the airplane is equal to the sum of the wind velocity and the velocity of the airplane relative to the wind. This results in 8 equations and 8 unknowns, which can be solved to find the values for the velocity of the airplane and the velocity of the wind.
  • #1
hellbike
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0

Homework Statement


Airplane flies over route in shape of triangle ABCD. Time(t1, t2, t3) of flying over sections AB, BC, CA are known. Lenght of sections is also known. During fly wind is present. velocity of wind is constant, and speed of airplane relative to wind is also constant.
Find velocity of airplane and velocity of wind.

Homework Equations


The Attempt at a Solution



I don't understand this problem. I can get velocity of airplane from |AB|/t1

There is no relation between velocity of airplane and velocity of air, and air can have any constant velocity.

Why am i wrong?
 
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  • #2
Hi hellbike! :smile:
hellbike said:
… velocity of wind is constant, and speed of airplane relative to wind is also constant.
Find velocity of airplane and velocity of wind
…
I don't understand this problem. I can get velocity of airplane from |AB|/t1

Yes, you're right … my guess is that the question is supposed to be asking for the speed of the airplane relative to wind, not for the velocity of the airplane …

you'd better go for that! :rolleyes: :wink:
There is no relation between velocity of airplane and velocity of air, and air can have any constant velocity.

Not following you :confused: … velocity of airplane = velocity of air + velocity of airplane relative to wind.
 
  • #3
I came up with solution, but not sure if this is enough.

v1 = |AB|/t1 , where t1 is time of flight over AB section. We know all sides of triangle, so we know angles, so we know direction of v1. this is a vector.
v2 ...
v3 ...

Vw - speed of wind (this is a vector and it's unknown)
Va - speed of plane relative to wind on first section (this is a vector and it's unknown)
Vb ...
Vc ...

and now
Vw + Va = V1
Vw + Vb = V2
Vw + Vc = V3

|Va|=|Vb|=|Vc| (because absolute value of plane relative to wind is constant)

are those equations enough (what I'm looking for in this problem is Vw and |Va|)?

since those vectors are two dimensional, that gives 8 equations and 8 unknowns. I think. But I'm not sure.
 
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  • #4
hellbike said:
… are those equations enough (what I'm looking for in this problem is Vw and |Va|)?

Yes!

Go for it! :smile:​
 

Related to Finding Velocity of Airplane & Wind: An Analysis of Triangle ABCD

1. What is the purpose of analyzing the velocity of an airplane and wind in triangle ABCD?

The purpose of this analysis is to understand the relationship between the velocity of an airplane and the velocity of the wind it is flying against. This information is crucial for pilots to make necessary adjustments to their flight path and ensure a safe and efficient journey.

2. How is the velocity of the airplane and wind measured in this analysis?

The velocity of the airplane is typically measured using instruments on the aircraft, such as an airspeed indicator. The velocity of the wind can be determined by looking at the direction and speed of nearby weather stations or using specialized equipment, such as a pitot-static system.

3. What factors can affect the accuracy of the velocity analysis in triangle ABCD?

There are several factors that can affect the accuracy of this analysis, including changes in weather conditions, variations in altitude, and the limitations of the measuring instruments. Additionally, human error in recording and interpreting the data can also impact the accuracy of the results.

4. What are some potential applications of this analysis?

Understanding the velocity of an airplane and wind can have various applications, such as improving flight safety and efficiency, developing more effective aircraft designs, and aiding in weather forecasting. This analysis can also be used for research purposes, such as studying the effects of wind on aircraft performance.

5. How does this analysis contribute to the field of aviation?

This analysis provides valuable insights into the complex relationship between an airplane and the wind it encounters during flight. By understanding this relationship, pilots and aviation professionals can make informed decisions to ensure a smooth and safe flight. It also contributes to the ongoing research and development in the field of aviation, leading to advancements in technology and safety measures.

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