Calculating Wind Velocity using Relative Velocity Formula | Easy Explanation

[Elysian]

Homework Statement

A Boeing is flying east at 150 km/hr, After 2 hours it is 350 km East and 74 km south of its starting point. What is the magnitude and direction of the wind velocity?

Homework Equations

Not sure if any

The Attempt at a Solution

Well I really had no idea what to do so i started by finding the resultant vector of the distance after 2 hours, which came out to be 357.8 KM at -.00369 degrees...

My guess is that since I found this, I could make a vector for 150 km/h, and a vector for 357.8 km and the resultant of that would be the Wind velocity vector, to get the angle and then use law of cosines, i would add 180 to the -.00369 degrees and then go forward with law of cosines..

I also just converted the new displacements given to velocities, using V = d/t to get a resultant of 178.4 km/h with the same angle

Does this sound right or just absolutely absurd.. I hate relative velocity problems with a passion so if anyone can explain them briefly in general it'd be very much appreciated.

 

[GrantB]

Suppose I run on a surface that can move under me. If I run at 10km/h east, and the surface moves me southeast as I run, from my reference frame, what does my vector look like?

In other words, what would the vector of the plane look like without any wind?

I would start there. Then I would deal with where the plane actually is, and finally find what the wind vector was.

 

[Elysian]

Thanks for the advice GrantB, What I did now was I took what it would look like after two hours (300 km) east, and put the vector sum of 357.8 km which is what it actually is and connected them with a vector which would be the Wind vector... The problem now though is i have no angles for this triangle to use law of sines or law of cosines to solve as its not a 90 degree triangle.

 

[GrantB]

Yeah I believe you will have to use the Law of Cosines.

You should be able to find the angle between the windless-plane and the wind-plane.

Glad I could be of help :]

 

[rwisz]

Your approach is on the right track. To calculate the wind velocity, we need to use the relative velocity formula, which states that the velocity of an object with respect to a frame of reference is equal to the difference between the velocity of the object and the velocity of the frame of reference. In this case, our frame of reference is the ground, and the object is the Boeing flying east at 150 km/hr.

To calculate the wind velocity, we first need to find the resultant vector of the distance traveled by the Boeing after 2 hours. This can be done by using the Pythagorean theorem: √(350^2 + 74^2) = 357.8 km. Now we can use the law of cosines to find the angle of this resultant vector, which is approximately -0.00369 degrees. This represents the direction of the wind velocity.

Next, we need to find the magnitude of the wind velocity. This can be done by subtracting the velocity of the Boeing (150 km/hr) from the resultant velocity (357.8 km/hr). This gives us a wind velocity of 207.8 km/hr.

So the magnitude of the wind velocity is 207.8 km/hr, and the direction is approximately -0.00369 degrees. This means that the wind is blowing from the east-southeast at a speed of 207.8 km/hr. I hope this helps to clarify the process of solving relative velocity problems. Remember to always use the relative velocity formula and break down the problem into smaller steps to make it easier to solve.