A plane is moving due north, directly towards it destination...physic problem..?

Question

A plane is moving due north, directly towards it destination. Its airspeed is 200 mph. A constant breeze is blowing from west to east at 20 mph. In which direction is the plane pointed.

The answer to this question is 5.7 degree W of N...but i dont know how to get that answer...can someone please explain...

Answer 1

Draw a triangle as follows:

Start at the planes strating point and draw a line a bit less then 200 units long stright up the paper. That's how the plane is traveling.

From the top of that line, draw a flat line (forming a 90 degree angle), 20 units to the LEFT. The wind blows this much.

Then connect the end point to starting point, this is the direction the plane is POINTED. In terms of this problem, it's 200 units long (the air speed of the plane).

Now consider: The plane is traveling up the diagonal 200 miles, and being pushed by the wind over 20 miles as it does so, so it ends up travelling north (the first line you drew). So all you need now is to find the angle at the base. See it?

You have 200 for the diagonal and 20 for the side. 20/200 = .1

Arcsine (.1) = 5.7 degrees (with a wee bit of rounding).

Hope that helps!

Answer 2

Draw the 'wind triangle`.
The course is due north. (Ground Speed unknown)
The wind correction leg is 20 MPH to the east(Correction for west wind).
The Heading, (hypotenuse and direction the plane is pointed), is "airspeed 200 MPH".
You have two sides and an included right angle.
You can solve for heading (and ground-speed as
well if they'd asked you).

Answer 3

The answer is N5.71'E.
tan-1 20/200 = tan-1 (0.1) = 5.71'

I do not know how to draw a diagram in the answer. Otherwise I can explain better.