Relative Velocity Problem - find the angle

[jtw2e]

Relative Velocity Problem -- find the angle

Homework Statement

An airplane has a cruising speed (speed of plane with respect to the air) of 547 mph. The wind is blowing at 84 mph 40° north of east. The plane needs to fly from Geordi to Data, which is 982 miles at 28° west of north.

Part A: What direction should the plane head to fly straight from Geordi to Data? (° W of N).

Part B: How long does it take for the plane to fly from Geordi to Data? (hours)

Homework Equations

Law of sines?

The Attempt at a Solution

http://www.flickr.com/photos/28413236@N03/5443668917/

Based on the figure I have made, which is probably incorrect if any pattern can be drawn from the previous 6 hours of failure:

I tried to use law of sines to find alpha:
84/sin(α) = 547/sin(50)

Using the inverse sine I get an angle of 6.76° for α. (This makes no sense as we're given that the direction from Geordi City to Data City is 28 degrees West of North. What is going on here?)

 

[white_is]

I had a similar problem to this. I came across this website and it helped me through it.

http://hyperphysics.phy-astr.gsu.edu/hbase/airpw3.html#c2

You can click on "Details about calculation" and it will give a little more explanation. Then you can click "More detail on calculation" and it gives you another picture and a couple equations.

At first I wasn't sure where the equations came from. But if you sit there and think about what they are saying it makes sense.

Sorry I can't be more help, I've having trouble with the rest of my homework lol.

 

[jtw2e]

I had a similar problem to this. I came across this website and it helped me through it.

http://hyperphysics.phy-astr.gsu.edu/hbase/airpw3.html#c2

You can click on "Details about calculation" and it will give a little more explanation. Then you can click "More detail on calculation" and it gives you another picture and a couple equations.

At first I wasn't sure where the equations came from. But if you sit there and think about what they are saying it makes sense.

Sorry I can't be more help, I've having trouble with the rest of my homework lol.

Thanks, what they're saying does make sense. My problem still is illusive to me.

 

[ehild]

You know alpha, it is the direction of Data from Georgi with respect to North. The resultant velocity is the vector sum of the aeroplane velocity with respect to air, and the velocity of wind. You get a triangle with two sides known, and one angle also known (50+28) apply the Sine Law to get x, and from that beta, the direction of the plane with respect to North.

ehild

 

[ashishsinghal]

the plane will acquire the velocity of the wind too. wind would change its path. so just think how can you remove the effect of wind