Flying between aircraft carriers - vectors

[princesspriya]

Homework Statement

You are a pilot on an aircraft carrier. You must fly to another aircraft carrier, now 1450 km at 45 degree of your position, moving at 56 km/hr due east. The wind is blowing from the south at 72 km/hr. Calculate the heading and airspeed needed to reach the carrier 2.5 hour after you take off.

Homework Equations

i drew a picture but i don't even know if i have the picture right or what to do from there on please help. http://img127.imageshack.us/my.php?image=physicsvo6.jpg

The Attempt at a Solution

 

[lippyka]

I drew the picture and i don't really know what to do from there. i tried using the law of cosine but im not sure how to use it for this kind of problem. Please help!

 

[Moetasim]

I would approach this problem by using vector analysis to determine the heading and airspeed needed to reach the other aircraft carrier. First, I would draw a diagram representing the situation, with the two aircraft carriers and the wind vector. From this diagram, I would break down the wind vector into its components (north-south and east-west) using trigonometric functions. Next, I would use vector addition to find the resultant vector of the wind and the carrier's velocity, which would give me the necessary heading to reach the other carrier. Finally, using the distance and time given, I can calculate the airspeed needed to reach the carrier in 2.5 hours. This approach allows for a systematic and accurate solution to the problem, taking into account all the relevant vectors and their components.