Vector Motion Problems: Finding Direction and Speed of a Plane

  • Thread starter zack558
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In summary, the plane should head in a direction of 45 degrees west of north to land at an airport north of its present location.
  • #1
zack558
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Homework Statement



An airplane has a speed of 265 km/h relative to the air. There is a wind blowing at 90 km/h at 30° north of east relative to Earth. In which direction should the plane head to land at an airport due north of its present location(in degrees west of north)?
What is the plane's speed relative to the ground (km/h)?

Homework Equations



Vx0 = V0cos(O)
Vy0 = V0sin(O)


The Attempt at a Solution



VwindE = 90cos(30) = 77.9 km/h
VwindN = 90sin(30) = 45 km/h

I am trying to figure out what to do from here. It says that the plane's velocity is 265 km/h, but it doesn't say which way the plane is going. I am clueless on what to do to get the direction the plane should head. I know I don't have a lot of steps, but I'm completely stuck.
 
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  • #2
Try to work out the problem, and show the steps.

One knows the air speed or speed of the airplane with respect to the air. One is trying to solve for the direction of the aircraft in the wind, in order to get to a destination. One knows the direction and speed of the wind.

Displacement vector = velocity vector * time.

Vector addition is part of the solution to this problem.
 
  • #3
This might also help you with these kind of problems:

You have three vectors a, b, c:
The wind velocity a=(a1,a2)
The velocity of the airplane through the air b=(b1,b2)
The velocity of the airplane along the ground c=(c1,c2)

The relationship between these vectors is a+b=c, which is equivalent to the two equations
a1+b1=c1
a2+b2=c2

The solution to one of these equations gives the direction of the plane. This direction, along with the other equation gives the planes ground speed.
 

1. What is a vector/motion problem?

A vector/motion problem is a type of problem in physics or mathematics that involves the use of vectors to describe the motion or movement of an object.

2. What is a vector?

A vector is a mathematical quantity that has both magnitude (size or length) and direction. It is often represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude.

3. How do you solve a vector/motion problem?

To solve a vector/motion problem, you must first determine the given information and identify the unknown variables. Then, you can use vector addition, subtraction, and other operations to find the solution. It is also important to draw a clear diagram and use the correct units for the vectors.

4. What are some common types of vector/motion problems?

Some common types of vector/motion problems include finding the resultant or net displacement of an object, calculating the velocity or acceleration of an object, and determining the angle or direction of a vector.

5. Why are vector/motion problems important?

Vector/motion problems are important because they help us understand and analyze the motion of objects in the real world. They are also used in various fields such as engineering, physics, and navigation.

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