Vector Motion Problems: Finding Direction and Speed of a Plane

[zack558]

Homework Statement

An airplane has a speed of 265 km/h relative to the air. There is a wind blowing at 90 km/h at 30° north of east relative to Earth. In which direction should the plane head to land at an airport due north of its present location(in degrees west of north)?
What is the plane's speed relative to the ground (km/h)?

Homework Equations

Vx0 = V0cos(O)
Vy0 = V0sin(O)

The Attempt at a Solution

VwindE = 90cos(30) = 77.9 km/h
VwindN = 90sin(30) = 45 km/h

I am trying to figure out what to do from here. It says that the plane's velocity is 265 km/h, but it doesn't say which way the plane is going. I am clueless on what to do to get the direction the plane should head. I know I don't have a lot of steps, but I'm completely stuck.

 

[Astronuc]

Try to work out the problem, and show the steps.

One knows the air speed or speed of the airplane with respect to the air. One is trying to solve for the direction of the aircraft in the wind, in order to get to a destination. One knows the direction and speed of the wind.

Displacement vector = velocity vector * time.

Vector addition is part of the solution to this problem.

 

[jimvoit]

This might also help you with these kind of problems:

You have three vectors a, b, c:
The wind velocity a=(a1,a2)
The velocity of the airplane through the air b=(b1,b2)
The velocity of the airplane along the ground c=(c1,c2)

The relationship between these vectors is a+b=c, which is equivalent to the two equations
a1+b1=c1
a2+b2=c2

The solution to one of these equations gives the direction of the plane. This direction, along with the other equation gives the planes ground speed.