SOLUTION: A plane is flying 400 miles per hour due North (Theta Angle is 90 degrees). A wind suddenly blows at 50 miles per hour from the West to the East (Theta Angle is 0 degrees) What

Algebra ->  Angles -> SOLUTION: A plane is flying 400 miles per hour due North (Theta Angle is 90 degrees). A wind suddenly blows at 50 miles per hour from the West to the East (Theta Angle is 0 degrees) What      Log On


   

Question 1022322: A plane is flying 400 miles per hour due North (Theta Angle is 90 degrees). A wind suddenly blows at 50 miles per hour from the West to the East (Theta Angle is 0 degrees)
What will be the new velocity of the plane, Angle Alpha & Angle Theta.
New velocity of plane is [1]
Angle Alpha is [2]
Angle Theta is [3]
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Addition of the two vectors; that of the plane and that of the wind.

(400*cos(90),400*sin(90))+(50*cos(0),50*sin(0))

( 400*cos(90)+50*cos(0), 400*sin(90)+50*sin(0) )

(0+50, 400+0)

( 50, 400 )

You can use this to find the angle, and to find the size of the rate.


Size of the rate, or speed, is sqrt%2850%5E2%2B400%5E2%29;
and the angle is tan%2840%2F5%29=tan%288%29, meaning arctan%288%29.
83.9 degrees North of Eastward.