An airplane flies horizontally from east to west at 320 mph relative to the air. If it flies in a steady 40-mi/hr wind that blow
s horizontally toward the southwest (45 degrees south of west). find the speed and direction of the airplane relative to the ground.
1 answer:
Answer:Speed of airplane= 43.18mi/he
Direction of the airplane relative to the ground=4.64°. Counter-clockwise rotation from west.
Step-by-step explanation: welovity/speed is represented as magnitudes of vectors.
Let A= the vector of the airplane
Let W= the vector of the wind
From the diagram,total vector F= A + w
F= 320+ 40cos45°I +0j) + (0i + 40sin46°)
F=320+28.28i+28.28j
To calculate the magnitude
/F/=root of A2 +w2
/F/=root320+40cos45°2+40sin45°2
/F/=root 1919.5168
/F/=43.18= speed
To calculate the direction of the airplane relative to the ground, use tan function because it is a right triangle as seen in the diagram
Tan x= opp/adj=40sin45/320+40cos45
Tanx=28.28/348.28
Tanx=0.091199
×=tan-1 0.091199
×=4.64
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