How Do You Calculate the Resulting Speed of a Plane Adjusting for Wind?

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Homework Help Overview

The problem involves calculating the resulting speed of a plane adjusting for wind. The plane is flying at a specified speed and angle, while the wind is blowing from a specific direction. The subject area includes vector decomposition and trigonometry.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss drawing a diagram to visualize the problem and consider using trigonometric functions to decompose the plane's velocity into components. There are attempts to apply the Pythagorean theorem to find the resultant speed. Some participants question the setup of the triangle and the components derived from the angle given.

Discussion Status

There are multiple interpretations of how to approach the problem, with some participants providing guidance on setting up vectors for the plane and wind. Others express uncertainty about their calculations and seek clarification on the methodology. The discussion is ongoing, with various lines of reasoning being explored.

Contextual Notes

Some participants mention constraints related to their prior knowledge and the specific format in which they were taught to solve similar problems. There is also a reference to the need for clarity on polar coordinates and vector representation.

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Homework Statement



A plane flies at 400 km/h [south 30 degrees east]. The wind is blowing from the east at 100 km/h. Find the resulting speed of the plane.

Homework Equations



Not sure

The Attempt at a Solution



I've drawn a diagram similar to this:

|\
| \
| \
|30\
| \
| \ 400 km/h
| \
|_____\
100km/h

I thought this was just a simple question of finding the left side of the triangle, but I don't seem to get the answer. Any hints is greatly appreciated.

Thank you in advance.
 
Last edited:
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You have drawn a 30-60-90 right triangle. If the hypotenuse is 400 km/hr, the base would be 200 km/hr, not 100 km/hr.

Decompose the plane's velocity into a south component and and east component.
 
Hmm so would this work?

use 30 degrees and 400 km/h to find the speed going straight south

cos (30) * (south_speed/400)
south_speed = cos(30) * 400 = 346

Then use speed going straight south and incorporate the 100km/h wind blowing west, use Pythagorean theorem and find the resultant speed(hypotenuse)?

346^2 + 100^2 = 130000^2
= 360.5

Does that seem right?
 
Set up a vector for the plane velocity: P = < ?, ?>
Write a vector for the wind velocity: W = <?, ?>

The resultant velocity is V = P + W and its length is the groundspeed.
 
Can you please show me how? I was only only taught how to do it when the points were given.
 
Whiz said:
Can you please show me how? I was only only taught how to do it when the points were given.

Think of the plane as at the origin with the x direction East and y direction North. The direction described as "South 30 degrees East" is the polar coordinate angle -60 degrees. So the plane velocity is given to you in polar coordinates, r = 400 and \theta = -\pi/3. Use the polar coordinate equations to get P = <x, y> for the airplane. And you should easily be able to write the wind vector since you are given its length 100 and direction "from the East".

By the way, I didn't say your answer was incorrect. I'm just trying to show you how you should set up such problems.
 
Last edited:
Whiz said:
Hmm so would this work?

use 30 degrees and 400 km/h to find the speed going straight south

cos (30) * (south_speed/400)
south_speed = cos(30) * 400 = 346

Then use speed going straight south and incorporate the 100km/h wind blowing west, use Pythagorean theorem and find the resultant speed(hypotenuse)?

346^2 + 100^2 = 130000^2
= 360.5

Does that seem right?
Yes, this is pretty close. I get a slightly larger figure since I didn't round off what you're calling south_speed, which I get as 346.41 km/hr (approx.).
 

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