2D Vector Work With Wind and Other Elements

[QuickSkope]

Homework Statement

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.

Homework Equations

Coslaw
Sin Law

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

 

[anathema]

I appreciate your detailed approach to solving this problem. However, I would like to provide some suggestions and corrections to your solution.

Firstly, in your first attempt, you mentioned using "Z law" to find the angle between the two carriers. I believe you meant to say "Pythagorean theorem" to find the hypotenuse of the triangle formed by the two carriers and the starting point. Additionally, you used the "Coslaw" and "Sinlaw" to find the distance and angle, respectively. I think you meant to say "Cosine law" and "Sine law."

Furthermore, in your second attempt, you mentioned using "Z law" again to find the angle. I believe you meant to say "Inverse tangent" or "Arctangent" to find the angle. Additionally, you mentioned using "Coslaw" and "Sinlaw" to find the speed and angle, respectively. Again, I believe you meant to say "Cosine law" and "Sine law."

In terms of your calculations, I noticed a few errors. In your first attempt, you divided the total distance by 2.5 hours to find the speed of the plane, which is incorrect. The correct approach would be to divide the total distance by the time of travel, which is 2.5 hours. This would give you the average speed of the plane, which is 620.88 km/h. Additionally, in your second attempt, you used the wrong angle (32.73 degrees) in your calculation for the speed of the plane relative to the ground. The correct angle to use would be the angle between the direction of the plane's motion and the direction of the wind, which is 45 degrees.

Finally, to find the heading and airspeed needed, you would need to add the wind speed (72 km/h) to the average speed of the plane (620.88 km/h) to get the airspeed. This would give you an airspeed of 692.88 km/h. To find the heading, you would use the inverse tangent (arctangent) function to find the angle between the direction of the plane's motion and the direction of the wind. This angle would be approximately 8.74 degrees.

In summary, your approach and understanding of the problem are correct, but there were some small errors in your calculations and terminology. I hope this helps clarify any confusion and improves your solution. Keep up the