Solving Plane Course & Speed Problems

[bluejeans]

Homework Statement

The course and ground speed of a plane are 70 degrees and 400 miles per hour respectively. There is a 60 mph wind blowing from the south. Find the approximate direction and air speed of the plane.

Homework Equations

net force = force1 + force2

The Attempt at a Solution

Net Direction = 70-60 = 10
Net Speed = 400- x = 10 x = 410
10 degrees and 410 speed. The teacher said that was wrong though, what am I doing wrong?

 

[kamerling]

Net Direction = 70-60 = 10
Net Speed = 400- x = 10 x = 410
10 degrees and 410 speed. The teacher said that was wrong though, what am I doing wrong?

You're subtracting the speed of the find from the direction of the ground speed. That makes no sense.

you have ground velocity = air velocity + wind velocity. All the velocities here are vectors with magnitude and direction. Separate them in a northward and an eastward component.

 

[Dick]

The problem is that you aren't doing much right. It looks like you are just combining numbers at random. You need to express all of these velocities as vectors, split them into NS and EW components. You must have done something like that before. Then you can solve the vector equation ground velocity=wind velocity+air velocity.

 

[Celunas]

I assume you can already use vectors (if not, I am not sure how I would do this question !)

The air speed is calculated with the plane as a frame of reference. It means you forget about the ground. Try to imagine you're flying this craft. Forgetting the wind, due to your ground speed, you feel a 400 mph wind in your face. It means that without wind, you would have a 400 mph airspeed. Now imagine you're in a helicopter, idle, but with wind. Forgetting the ground and the fact you're idle, you feel a 60 mph wind heading to the north, which gives you the feeling that you're flying at the same speed to the south, without wind, with your craft as a frame of reference.
So you feel 2 different speeds only due to the wind, forgetting the ground, one at 400 mph heading 70°, and one heading south at 60 mph.
You can represent these two speeds as vectors.

Try to find the coordinates of both vectors, and add them to find the net airspeed vector ! Then calculate its magnitude (the net airspeed) and the angle between it and the north (the net direction)

 

[jimvoit]

A tutorial in 2D vectors would help you out.

Ask your instructor for a reference on how to work with 2D vectors. For this problem you need to:

Express the wind velocity as a vector.
Express the aircraft velocity through the air as a vector.
Add the vectors.
Determine the magnitude of the resulting vector (pythagorean theorem)
Determine the direction of the resulting vector (arc tangent function)

Directions can be confusing in navigation problens because they are measured positive clockwise from north instead of positive counterclockwise from the x-axis of the conventional 2D Cartesian coordinate system.