How Does Wind Affect Airplane Groundspeed and Flight Angle?

[bricker9236]

Homework Statement

a small airplane flies at a max airspeed of 255km/hr. (velocity relative to air). The wind is blwoing from the north at 63km/hr. The pilot heads this plane at a heading 41degrees south of straight east.

a) what is the planes groundspeed (the velocity that the plane will travel relative to the ground)?

b) relative to the gorund, the plane moves at an angle south of east. What is the angle measured in degrees from due east?

Homework Equations

WAS very confused on this problem.
for part a i just figured out the V for plane - 255/sin 131
255/cos131
and then the V air - 63/sin 180
v air- 63/cos 180

then took the square root of (192.5+ -230.3)

for part b I just took the tan of -230.3/192.5= -50 degrees

The Attempt at a Solution

a) i got the answer 300km/hr who knows if that is right.
b) 50degrees south of east or 140 degrees. again no idea if that is near the correct answer

 

[Andrew Mason]

Homework Equations

WAS very confused on this problem.
for part a i just figured out the V for plane - 255/sin 131
255/cos131
and then the V air - 63/sin 180
v air- 63/cos 180

then took the square root of (192.5+ -230.3)

for part b I just took the tan of -230.3/192.5= -50 degrees

The Attempt at a Solution

a) i got the answer 300km/hr who knows if that is right.
b) 50degrees south of east or 140 degrees. again no idea if that is near the correct answer

Draw a vector diagram. What is the relationship between the three velocity vectors (plane:wind; wind:ground; plane:ground)? Write that out as an equation.

Find the components of the plane:ground vector in the NS and EW directions.

Use Pythagoras to find the length and arctan of the NS/EW components to find the angle (from the EW axis).

Your answer is right but you seem to be confused about how you got it. If you follow the above, you will avoid confusion.

AM