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

[hellbike]

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?

 

[tiny-tim]

Hi hellbike!

… 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!

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

Not following you … velocity of airplane = velocity of air + velocity of airplane relative to wind.

 

[hellbike]

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.

 

[tiny-tim]

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

Yes!

Go for it! ​