Basically we were given vector problems, HELP

  • Thread starter kushalksoni
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In summary, to calculate the airspeed and heading needed for a pilot to achieve a groundspeed of 260mph on a bearing of 180 degrees, the concept of vector addition should be used. Splitting the wind and desired groundspeed into north-south and east-west components, the airspeed can be found using the Pythagorean theorem. The heading can then be calculated using the tangent function, depending on the desired compass reading format.
  • #1
kushalksoni
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Homework Statement


A pilot wants his groundspeed to be 260mph on a bearing of 180 degrees. An east wind is blowing at 65mph. What should his airspeed and heading be so that the wind will blow him back onto his intended course?


Homework Equations





The Attempt at a Solution


I drew it out, but apparently its wrong. I drew a right triangle with the wind as the horizontal and 260mph as the vertical and that's all i got. Please explain with concept too. Thanks
 
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  • #2
Concept is called vector addition. The unknown desired heading should be the vector that when added to "east wind is blowing at 65mph" yields, "260mph on a bearing of 180 degrees". Split them into NS and EW components.
 
  • #3
kushalksoni said:

Homework Statement


A pilot wants his groundspeed to be 260mph on a bearing of 180 degrees. An east wind is blowing at 65mph. What should his airspeed and heading be so that the wind will blow him back onto his intended course?


Homework Equations





The Attempt at a Solution


I drew it out, but apparently its wrong. I drew a right triangle with the wind as the horizontal and 260mph as the vertical and that's all i got. Please explain with concept too. Thanks
Nothing wrong with that. Taking "east" to the right and "south" downward, draw a line to the right with length "65 mph" and, at the end of that, draw a line downward with length "260 mph". That gives you a right triangle with legs of length 65 and 260. The airspeed is the length of hypotenuse. The Pythagorean theorem gives you that. Which angle you use depends on how you want to write the course. If you want to write it as a compass reading in degrees from north, it will be 90 plus the angle in the upper left of the triangle, where you started. If you want to write it as "degrees east of south", it will be 90 degrees minus that angle. In either case you can use the tangent function to find "that angle".
 

1. What are vector problems?

Vector problems involve using vectors, which are mathematical quantities that have both magnitude (size) and direction, to solve various mathematical and scientific problems. They are commonly used in physics, engineering, and other fields.

2. How do I approach vector problems?

The first step in solving vector problems is to identify the given quantities, such as vector magnitudes and directions. Then, you can use mathematical operations, such as addition and subtraction, to manipulate the vectors and find the desired solution.

3. What are some common types of vector problems?

Some common types of vector problems include finding the resultant or net vector from multiple given vectors, analyzing motion and forces in physics, and solving optimization problems in mathematics.

4. What are some useful tools for solving vector problems?

Some useful tools for solving vector problems include vector diagrams, trigonometry, and vector algebra. These can help you visualize and manipulate the given vectors, making it easier to find the solution.

5. How can I improve my skills in solving vector problems?

The best way to improve your skills in solving vector problems is to practice regularly and familiarize yourself with different types of vector problems. Additionally, studying the concepts and formulas related to vectors can also help you become more proficient in solving these types of problems.

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