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Crosswinds A small plane is flying horizontally due east
Chapter 10, Problem 45E(choose chapter or problem)
Crosswinds A small plane is flying horizontally due east in calm air at 250 mi/hr when it is hit by a horizontal crosswind blowing southwest at 50 mi/hr and a 30-mi/hr updraft. Find the resulting speed of the plane and describe with a sketch the approximate direction of the velocity relative to the ground.
Questions & Answers
QUESTION:
Crosswinds A small plane is flying horizontally due east in calm air at 250 mi/hr when it is hit by a horizontal crosswind blowing southwest at 50 mi/hr and a 30-mi/hr updraft. Find the resulting speed of the plane and describe with a sketch the approximate direction of the velocity relative to the ground.
ANSWER:Solution 45E
Step 1:
First you find x, y components of the wind. Assuming it is exactly southwest
x = -50cos(π/4) … it is negative since it’s westerly wind
= -50
= -25
Combining the speed of the plane and the wind
x = 250 - 25
= 214.64
y = -25 … the plane does not have the y component
Resultant speed is
v =
= 217.54
Φ = -arccos(214.64/217.54) … angle from x-axis; south of east
= -0.163 rad
= -9.37°
Now we add the updraft component.
v =
= 219.60
θ = π/2 - arccos(217.54/219.60) … measured from vertical
= 1.433 rad
= 82.14°
The resultant speed of the plane is 219.60 mph, 1.433 rad (82.14°) from zenith, 0.163 rad (9.37°) south of east.