Vectors in the Plane: Plane+Wind question

In summary, the conversation discusses the calculation of groundspeed and direction for an airplane with an airspeed of 430 mph at a bearing of S 45 degrees E, and a wind of 35 MPH in the direction of N 30 degrees E. The solution involves using the equation [[v]]([cos theta], [sin theta]) and the result is a groundspeed of 440.3 mph. There is some uncertainty about the accuracy of this solution due to a possible typo in the book.
  • #1
pugfug90
118
0

Homework Statement


An airplane has an airspeed of 430 mph at a bearing of S 45 degrees E. If the wind is 35 MPH in direction of N 30 degrees E, find groundspeed and direction of plane.


Homework Equations


[[v]]([cos theta], [sin theta])


The Attempt at a Solution



430(cos 315,sin315)+35(cos30,sin30)=?<334.4,-286.6>
[[v]]=?~440..

Back of book says that the ground speed is 422.3.. and if i go the vector wrong, that means magnitude and direction will be wrong also.. Where did I go wrong?
 
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  • #2
If the numbers you give are correct, then you have it right. The ground speed is 440.3, not 422.3.
 
  • #3
Hope you're right. This isn't the 1st time the book has a typo or something.
 

1. What is a vector in the plane?

A vector in the plane is an object that has both magnitude and direction. It is typically represented by an arrow with a specific length and direction. In mathematics and physics, vectors are used to represent quantities such as velocity, force, or displacement.

2. How do you add two vectors in the plane?

To add two vectors in the plane, you must first determine their components (magnitude and direction) and then use the rules of vector addition. This involves adding the corresponding components of the vectors to get a new vector with a resulting magnitude and direction. This can also be visualized as placing the tail of one vector at the head of the other and drawing a new vector from the tail of the first vector to the head of the second.

3. Can vectors in the plane have negative components?

Yes, vectors in the plane can have negative components. This indicates that the vector is pointing in the opposite direction of the positive component. For example, a vector with a negative x-component would point in the negative x-direction.

4. What is the difference between displacement and distance in relation to vectors in the plane?

Displacement is the straight-line distance and direction between an object's starting point and ending point. It is represented by a vector in the plane. Distance, on the other hand, is the total length of the path traveled by an object and is a scalar quantity.

5. How does wind affect vectors in the plane?

Wind can affect vectors in the plane by changing the direction or magnitude of the vector. For example, the wind blowing against a plane's direction of motion would result in a decrease in the plane's velocity and a change in its direction. This can be taken into account when performing vector addition or when calculating quantities such as displacement or velocity.

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