An airplane flies at an air speed of 300 miles per hour, in the direction toward southwest. There is a head wind of 75 mi/hr in the direction toward due east. (A) Determine the ground speed. (B) Determine the direction of motion of the plane, expressed as an angle counterclockwise from due east.

Question

An airplane flies at an air speed of 300 miles per hour, in the direction toward southwest. There is a head wind of 75 mi/hr in the direction toward due east.  (A) Determine the ground speed. (B) Determine the direction of motion of the plane, expressed as an angle counterclockwise from due east.

shamim · Answer

its a problem of vector

shamim · Answer

i thnk its a 2 dimensional problem

shamim · Answer

i think u missed the angle of ur plane velocity 300 mile/hr with the ground

anonymous · Answer

Choose East as positive x-direction, North is positive y-direction
Velocity of the plane ( vector notation ) = -300*sin45 (x) -300*cos45 (y) mi/h
(x) : noted as x-direction, (y) : noted as y-direction, - negative sign indicates negative directions.
Velovity of the wind = 75 (x)  mi/h
(A) the ground speed = Square root of (V(airplane)^2 + V(wind)^2)
                                 =  Sqr of ((-212.13 + 75)^2 (x) + (-212.13)^2 (y))
                                  = 252.6 mi/h
(B) To determine the direction counterclockwise due to East, use tangent equation to fine the angle due to East. 
Ground velocity (in vector notation)= -137.3 (x) - 212.13 (y)
Angle & ---> Tan(&) = y/x =1.545 -----> & = Tan^-1(1.545)=57 degree
This is the angle between South and West, but we want to find the angle due to East. So the angle we want = 180-57 =123 degree due east