# Homework Help: 2D Vector Work With Wind and Other Elements

1. Apr 4, 2012

### QuickSkope

1. The problem statement, all variables and given/known data

You are a pilot on an F-16, waiting on a still aircraft carrier. You must fly to another aircraft carrier 1450 at 45* from your position, moving at 56 km/h due east. The wind is blowing from the south (To the north) at 72 km/h. Calculate the heading and air speed needed to reach the carrier 2.5h after you take off.

2. Relevant equations
Coslaw
Sin Law

3. The attempt at a solution

I took the question and broke it up into 2 questions. In 2.5 Hours, the Carrier will be 140 km from where it started, which was originally 1450 km away. I used Z law to find the angle in between and Coslawed to find the total distance you have to travel, and Sinlaw for the angle at which he traveled, then subtracted the angle of the triangle with the 45*. I found the Total distance was 1552.2 km and the angle was 32.73* N of E WITHOUT factoring the air in.

Work:
http://i866.photobucket.com/albums/ab228/QuickSkope/PhysicsBonus3Part2.jpg

Now, for part 2 I took my Resultant from part one, and added the wind speed to find the heading id need. To do this, again I used Z law to find the angle, and knowing that 1552.2 was the total distance between, I divided by 2.5 h and found the speed to be 620.88 km/h. Now with the speed of the plane relative to the air, and the speed of the air relative to the ground, I was able to find the speed of the plane relative to the ground using the angle I figured out (57.27*) and the 2 speeds beside (620.88 and 72, Plane and wind respectively). I did this using Coslaw, and found out that the speed was 585.1 km/h. Then I used sinlaw to find the angle, subtracting it from the 32.73 and found the actual angle needed, which was 25.7* N of E.

Work:
http://i866.photobucket.com/albums/ab228/QuickSkope/PhysicsBonus3Part1.jpg

My Question is: Is it right? Or did I do it horribly wrong :S