Lesson Flying airplane, blowing wind, airspeed, groundspeed etc.
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<H2>Flying airplane, blowing wind, airspeed, groundspeed etc.</H2 <H3>Problem 1</H3>A plane is steering at S65°W at an airspeed of 625 km/h. The wind is from the NW at 130 km/h. Find the groundspeed and track of the plane. <pre> <U>E x p l a n a t i o n</U> (1) Groundspeed is an aircraft's actual speed and direction of travel over the Earth's surface, calculated by combining the aircraft's true airspeed with the wind's velocity. Groundspeed is a vector sum, meaning both the speed and the direction of the wind are considered. (2) In aviation, airspeed is the speed of an aircraft relative to the air it is flying through. (3) "S65°W" refers to a bearing or direction, meaning South 65 degrees West. This notation indicates a direction starting from South and then rotating 65 degrees towards the West." <U>S O L U T I O N</U> So, S65°W is the direction of 270° - 65° = 205° in the standard coordinate plane. The direction of the wind "from NW" is 135° + 180° = 315° in the standard coordinate plane. Thus, we are given two vectors the airspeed of the plane = 625*(cos(205°), sin(205°)) km/h; (1) the wind speed vector = 130*(cos(315°), sin(315°)) km/h. (2) Let the groundspeed of the plane be (x,y). The groundspeed is the sum of the vectors (1) and (2) x = 625*cos(205°) + 130*cos(315°) = 625*(-0.90630778703) + 130*(+0.70710678118) = -474.5184853 km/h; y = 625*sin(205°) + 130*sin(315°) = 625*(-0.42261826174) + 130*(-0.70710678118) = -356.0602951 km/h. So, the groundspeed magnitude is {{{sqrt(x^2+y^2)}}} = {{{sqrt((-474.5184853)^2 + (-356.0602951)^2)}}} = 593.2509812 km/h. The angle of the vector with the x-direction of the coordinate plane is a = {{{pi}}} + {{{arctan(y/x)}}} = {{{pi}}} + {{{arctan((-356.0602951)/(-474.5184853))}}} = {{{pi}}} + {{{arctan(0.750361)}}} = {{{pi}}} + {{{0.643732}}} = = 3.14159265 + 0.643732 = 3.78532465 radians = 216.883127 degrees. <U>ANSWER</U>. The groundspeed magnitude is about 593.251 km/h. The direction of the groundspeed is about 216.883 degrees counterclockwise from positive direction of x-axis, or 90 - 36.883 = 53.117 degrees from South to East (S53.117°W). </pre> My introductory lessons on vectors in this site are - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Vectors-in-a-plane.lesson>Vectors in a plane</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Sum-of-the-vectors-that-are-coherently-oriented-sides-of-a-convex-closed-polygon.lesson>Sum of vectors that are coherently oriented sides of a convex closed polygon</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Sum-of-the-vectors-that-are-coherently-oriented-sides-of-an-unclosed-polygon.lesson>Sum of vectors that are coherently oriented sides of an unclosed polygon</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Sum-of-the-vectors-that-connect-the-center-of-a-parallelogram-with-its-vertices.lesson>Sum of vectors that connect the center of a parallelogram with its vertices</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Vectors-in-a-coordinate-plane.lesson>Vectors in a coordinate plane</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Addition-Subtraction-and-Multiplication-by-a-number-of-vectors-in-a-coordinate-plane.lesson>Addition, Subtraction and Multiplication by a number of vectors in a coordinate plane</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Summing-vectors-that-are-coherently-oriented-sides-of-a-convex-closed-polygon.lesson>Summing vectors that are coherently oriented sides of a convex closed polygon</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Summing-vectors-that-are-coherently-oriented-sides-of-an-unclosed-polygon.lesson>Summing vectors that are coherently oriented sides of an unclosed polygon</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/The-Centroid-of-a-triangle-is-the-Intersection-point-of-its-medians.lesson>The Centroid of a triangle is the Intersection point of its medians</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/The-Centroid-of-a-parallelogram-is-the-Intersection-point-of-its-diagonals.lesson>The Centroid of a parallelogram is the Intersection point of its diagonals</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Sum-of-the-vectors-connecting-the-center-of-mass-of-a-triangle-with-its-vertices.lesson>Sum of vectors connecting the center of mass of a triangle with its vertices</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Sum-of-the-vectors-connecting-the-center-of-mass-of-a-quadrilateral-with-its-vertices.lesson>Sum of vectors connecting the center of mass of a quadrilateral with its vertices</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Sum-of-the-vectors-from-the-center-of-mass-of-the-n-sided-polygon-to-its-vertices.lesson>Sum of vectors connecting the center of mass of a n-sided polygon with its vertices</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Sum-of-vectors-connecting-the-center-of-a-regular-polygon-with-its-vertices.lesson>Sum of vectors connecting the center of a regular n-sided polygon with its vertices</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Solved-problems-on-vectors-in-a-plane.lesson>Solved problems on vectors in a plane</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Solved-problems-on-vectors-in-a-coordinate-plane.lesson>Solved problems on vectors in a coordinate plane</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-find-the-length-of-the-vector-in-a-coordinate-plane.lesson>HOW TO find the length of the vector in a coordinate plane</A> - Flying airplane, blowing wind, airspeed, groundspeed etc. this lesson - <A HREF=https://www.algebra.com/algebra/homework/Vectors/REVIEW-of-Introductory-lessons-on-vectors-in-a-plane.lesson>OVERVIEW of Introductory lessons on vectors in a plane</A> Use this file/link <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A> to navigate over all topics and lessons of the online textbook ALGEBRA-II.
