Kinematics Vectors and cartesian coordinates. Plane with wind blowing.

In summary, the problem involves determining the ground speed and direction of motion of an airplane flying at an air speed of 300 miles per hour with a head wind of 75 mi/hr. To find the ground speed, decompose the vectors into x and y components, add them, and then recompose into the final vector. To find the direction of motion, use the equation θ = 180 + arctan|Vy/Vx|, where Vy and Vx are the y and x components of the final vector.
  • #1
freddyb
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Homework Statement



An airplane flies at an air speed of 300 miles per hour, in the direction toward southwest. There is a head wind of 75 mi/hr in the direction toward due east.
(A) Determine the ground speed.

(B) Determine the direction of motion of the plane, expressed as an angle counterclockwise from due east.


Homework Equations



Va=airspeed
w=wind speed
V=velocity relative to ground

V=(w-Va/sqrt2)i+(-Va/sqrt2)j

*i & j are constants

direction θ = 180 + arctan|Vy/Vx|



The Attempt at a Solution



Totally stumped any help would be greatly appreciated!
 
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  • #2
Decompose vector 1 into x & y components, add vector 2, recompose into final vector.
 

Related to Kinematics Vectors and cartesian coordinates. Plane with wind blowing.

1. What is kinematics?

Kinematics is the branch of physics that deals with the study of motion without considering the forces causing the motion.

2. What are vectors?

Vectors are quantities that have both magnitude and direction. They are represented graphically by arrows, with the length of the arrow showing the magnitude and the direction of the arrow showing the direction.

3. How are cartesian coordinates used in kinematics?

Cartesian coordinates are used to describe the position of an object in a plane. In kinematics, they are used to track the position of an object as it moves in a particular direction.

4. What is the significance of a plane with wind blowing in kinematics?

In kinematics, a plane with wind blowing represents a scenario where an object is moving in a two-dimensional plane while being affected by an external force, in this case, the wind. This scenario is often used to study the effect of external forces on an object's motion.

5. How does the wind affect an object's motion in a plane with wind blowing?

The wind affects an object's motion in a plane with wind blowing by changing its velocity. The direction and magnitude of the wind will determine the resulting change in the object's velocity, which in turn affects its position and trajectory in the plane.

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