Homework Help: Relative Velocity

1. Sep 14, 2004

psuedomonas

I just found this site, AWESOME.

Im having a problem this problem dealing with vectors:

An airplane has a veloctiy of 300mph going North of East, and the wind is blowing eastward at a velocity of 100mph at an angle of 45 degrees from east, what is the plane's new velocity?

is V naught= to 300(cos45) ? (the new velocity?)

Because using relative velocity addition is not coming up with the right answer, 300 is obviously the hypotenuse of this R triangle, I am stuck. I know the answer (360mph) I dont know how to work the problem to get the correct answer!! Help!!!

2. Sep 14, 2004

geometer

I think we need some more information here. How much north of east is the plane flying. In other words, at what angle with respect to the east axis is the plane flying and is the wind at 45 degrees north of east or south of east?

3. Sep 14, 2004

geometer

As a general procedure though, break the planes velocity into its north and east components, break the winds velocity into its north and east components, add these components to get the resultant vector.

If the plane is flying at angle A with respect to the East axis, then the north component of the plane's velocity is n = 300sinA, and the east component of the plane's velocity would be e = 300cosA. You can apply the same procedure to the wind's velocity.

4. Sep 14, 2004

psuedomonas

Sorry, I think I was over-anxious to get helped and misworded the question:

Plane moving initially at 300mph due East enters region where wind blowing 100mph in a direction 30 degrees North of East. What is new velocity of plane relative to the ground.

Sorry, boy...I really did a job on this question on my first post. :yuck:

5. Sep 14, 2004

geometer

The procedure is the same. Since the plane is flying directly east, its northern velocity component is 0. You need to resolve the wind's velocity into northern and eastern components and then add the plane's and the wind's velocity vector to get the resultant velocity. Find the magnitude of this vector and you have your answer.