Question 816597: I have a trig problem involving vector operations.
[ An airplane has an airspeed of 150 km/h. It is to make a flight in a direction of 70 degrees while there is a 25 km/h wind [TO] 340 degrees. What will the airplane's actual heading be? ]
NOTE: the original problem stated that the wind was FROM 340 degrees, but that is impossible assuming that the given result of 60 degrees is the solution to the problem. To obtain the result of 60 degrees, the wind must be TO 340 degrees, not FROM 340 degrees.
The answer is 60 degrees
how did my instructor figure it out?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! use vector addition:
a = magnitude 150 kph direction to 70 degrees
w = magnitude 25 kph direction to 340 degrees
---
convert angles from true north (aviation format), to polar coordinates:
70 degrees true north = +20 degrees polar
340 degrees true north = +110 degrees polar
---
calculate the rectangular coordinates of each vector:
---
a vector:
ay:
sin( 20 ) = opp/hyp
sin( 20 ) = ay/150
ay = 150 * sin( 20 )
---
ay = 51.303
---
ax:
cos( 20 ) = adj/hyp
cos( 20 ) = ax/150
ax = 150 * cos( 20 )
---
ax = 140.953
---
w vector:
wy:
sin( 110 ) = opp/hyp
sin( 110 ) = wy/25
wy = 25 * sin( 110 )
---
wy = 23.492
---
wx:
cos( 110 ) = adj/hyp
cos( 110 ) = wx/25
wx = 25 * cos( 110 )
---
wx = -8.551
---
calculate the result vector, from vector addition in rectangular coordinates
r vector:
rx:
rx = ax + wx
rx = 140.953 - 8.551
---
rx = 132.402
---
ry:
ry = ay + wy
ry = 51.303 + 23.492
---
ry = 74.795
---
convert r vector to polar coordinates:
rmag = sqrt( 132.402^2 + 74.795^2 )
rmag = 152.067 kph
rang = arctan( 74.795 / 132.402 )
rang = 29.462 degrees
convert polar angle to aviation format (true north)
rang = 60.538 degrees
---
Answer:
the airplane's actual heading after wind correction is 60.538 degrees, and its ground speed accounting for wind is 152.067 kph
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Convert fractions, decimals, and percents:
https://sooeet.com/math/fraction-decimal-percent.php
---
Calculate and graph the linear regression of any data set:
https://sooeet.com/math/linear-regression.php
|
|
|
