# What are the new speed and direction of the plane relative to the grou

1. Jan 26, 2010

### philok

1. The problem statement, all variables and given/known data
a plane moving initially at 300mi/h to the east, suddenly enters region where the wind is blowing at 100 mi/h toward the direction 30 degree's north of east. What are the new speed and direction of the plane relative to the ground.

2. Relevant equations

Magnitude= sqrt(A^2 + B^2 - 2ABcos ([STRIKE]0[/STRIKE]))
Angle= [STRIKE]0[/STRIKE] = tan-1(B/A)

3. The attempt at a solution

This is suppose to be a pretty straight forward question but Im not getting it. I first tried the first equation A=300 B=100. I am not coming up with the answer.

2. Jan 26, 2010

### edziura

Re: vectors

The soln is the sum of the two vectors (300 m/h E + 100m/h 30 deg N of E). Draw the first vector (arrow), then the second beginning with its tail at the tip of the first. Complete the triangle, then use triangle trigonometry to find the magnitude and direction of the third side. Alternatively, write both vectors in terms of their rectangular components and find the resultant that way.

3. Jan 26, 2010

Re: vectors