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What is a ground speed vector?
I've been working on an airplane + wind vector problem, and I'm not sure what ground speed vector means. Here's the question:
Tom is a pilot. His destination is located 200km south. Tom expects to fly at 180km/h. The wind is blowing from the West at 35km/h. Find the ground speed vector of the plane.
I understand that the ground speed vector is the sum of the plane's original vector and the wind's vector; so the vector for the plane affected by the wind. However, my teacher is telling me that the ground speed vector is the sum of the wind's vector and the vector of the plane affected by the wind. In this case, that would be the plane's vector unaffected by the wind.
I am super confused! Help!
1 Answer
- az_lenderLv 76 years ago
The ground speed vector should point south so that he will get to his destination. The question is, at what ground-speed will he actually make progress? It won't be 180 km/hr, as he must head somewhat southwest to achieve a southward ground speed. The westward COMPONENT of his airspeed must be 35 km/h, so if A is the angle between due south and his airspeed direction, then 35 = 180*sin(A) => sin(A) = 35/180. The southward component of his airspeed is 180*cos(A), and cos(A) = sqrt(1-sin^2(A)) = (1/180)*sqrt(180^2 - 35^2) = (1/180)*sqrt(32400-1225). So the southward component of his airspeed is sqrt(32400-1225) = sqrt(30175) = 173.71 km/h. His groundspeed vector is 173.71 km/h, due south.