Two airplanes taxi as they approach the terminal. Plane 1 taxies with a speed of
ID: 1957117 • Letter: T
Question
Two airplanes taxi as they approach the terminal. Plane 1 taxies with a speed of 11.0 m/s due north. Plane 2 taxies with a speed of 7.1 m/s in a direction 19.7° north of west.(a) What is the direction of plane 1 relative to plane 2?
Direction _______ north of east
(b) What is the direction of plane 2 relative to plane 1?
Direction _______ south of west
I found that for a.) the magnitude is 10.82 m/s. That is 8.517x and -6.6718y. I did
tan(-1) (-6.6718/8.571)=-37.89 degrees. Unfortunately this was wrong. Therefore, I did not even attempt b.). PLEASE HELP!
Explanation / Answer
(1) V12 = V1g + Vg2 (subscript 1g means 1 relative to ground, etc)
= V1 - V2
= 11.0 j - (7.1*cos19.7 (-i) + 7.1sin19.7 j)
= 6.68 i + 8.61 j
vector is in first quadrant, so
= tan-1(8.61/6.68) = 52.19 degrees north of east
(2) V21 = V2 - V1 = -6.68 i - 8.61 j
vector is in III quadrant, so
= tan-1 (8.61/6.68) = 52.19 degrees south of west