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

 

[tomcue]

.

I would like to clarify a few things in your solution. Firstly, it is important to note that the plane's velocity relative to the air and its velocity relative to the ground are two different things. The plane's velocity relative to the air is its airspeed, which is given as 255km/hr. This does not change regardless of the wind direction.

To find the groundspeed of the plane, we need to use vector addition. We can break the plane's velocity into two components - one in the east direction and one in the south direction. The east component will be 255*cos(41) = 192.5 km/hr and the south component will be 255*sin(41) = 165.3 km/hr. The wind's velocity can also be broken into two components - one in the east direction and one in the south direction. The east component of the wind is 63*cos(90) = 0 km/hr and the south component is 63*sin(90) = 63 km/hr.

Now, we can add the two vectors to get the resultant velocity, which will be the groundspeed of the plane. The east component will be 192.5 + 0 = 192.5 km/hr and the south component will be 165.3 + 63 = 228.3 km/hr. Using the Pythagorean theorem, we can find the magnitude of the resultant velocity, which is the groundspeed of the plane. This comes out to be approximately 296 km/hr, which is the correct answer for part a.

For part b, we need to find the angle at which the plane is moving relative to the east direction. To do this, we can use trigonometric ratios. The angle will be the inverse tangent of the south component divided by the east component. This comes out to be approximately 51.5 degrees south of east, which is the correct answer for part b.

I hope this explanation helps you understand the problem better. Remember, as a scientist, it is important to be precise and accurate in our calculations and explanations. Keep practicing and you will get better at solving such problems!