Question

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 blows horizontally toward the southwest (45 degrees south of west). find the speed and direction of the airplane relative to the ground.

Answer 1

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