"An aircraft going from Atlanta, GA to New York, NY on a bearing of S69oE is traveling at a speed of 430 miles per hour. The wind is blowing out of the north to south at a speed of 25 miles per hour. Find the ground speed and the plane's true bearing."
Is there any easy way to figure out problems like that?
My wonderful College thinks it's students can teach themselves how to solve that over the Internet without an instructor. :-(
May 12th 2005, 03:36 PM
If you don't mind doing it graphically.
An easy way to do it is to determine the two vectors, (size and direction) and add them.
Put the first one starting at the origin going S69oE size of 430. Then put the begining of the second one at the end of the first one, S at 25.
Give it a try, I can help further if you need.
The green vector in the picture below is your resultant vector.
If you break up the two vectors into horizontal and vertical componants you can use pythagorus' therom to solve for the resultant
June 14th 2009, 02:15 AM
The path of the wind, the light blue line in Math Help's picture, is parallel to the vertical axis so by "corresponding angles" with parallel lines the angle it makes with the red line is congruent to the angle the red line makes with the horizontal line, and is 90- 69= 21 degrees. The angle inside the triangle there is 180- 21= 159. You can use the cosine law to find the length of the opposite side, the ground speed of the airplane, and then use the sine law to find the angle at the top of the triangle. The angle the path of airplane makes with the horizontal is that angle plus 21 degrees.
But I don't think they are going to get from Atlanta to New York City on the heading!