# Question #5d46f

##### 1 Answer

#### Explanation:

**For this problem, I'll take the positive #x#-direction as east, and the positive #y#-direction to be *north***.

We're asked to find

(a) the direction the plane must face so that it travels to the island in a straight line

(b) its speed (which I'll assume is the speed *relative to the earth*)

We now know the plane has a velocity of *relative to the air* (not affected by wind).

The velocity components of the *wind* relative to the earth are

(it's traveling west, and thus has no vertical component)

The components of the plane's velocity relative to the air are

If we factor in the wind, the plane's velocity components relative to the **earth** are

We can use the trigonometric relationship

where

So, plugging in values, we have

Neglecting units:

So,

What we can do is graph the two equations

and

(**make sure your calculator is in degree mode**)

and find where they intersect; the

Now, using this angle and the velocity components, we can find the speed of the airplane relative to the earth:

The speed