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

AI Thread Summary
To find the new speed and direction of the plane relative to the ground, the initial velocity of 300 mi/h east must be combined with the wind velocity of 100 mi/h at a 30-degree angle north of east. The solution involves vector addition, where the two velocities are represented as vectors. By using trigonometry, one can calculate the resultant vector's magnitude and direction. The process includes drawing the vectors, completing the triangle, and applying the appropriate equations to determine the final speed and angle. The discussion emphasizes the importance of correctly applying vector addition techniques to solve the problem.
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Homework Statement


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.


Homework Equations



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

The Attempt at a Solution



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


Show your calculations.
 


OK got it. Thanks!
 

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