Velocities have both direction and magnitude and thus are vectors. The magnitude
ID: 1531508 • Letter: V
Question
Velocities have both direction and magnitude and thus are vectors. The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N 60 degree W at a speed of 80 km/h. (This means that the direction from which the wind blows is 60 degree west of the northerly direction.) A pilot is steering a plane in the direction N 45 degree E at an airspeed (speed in still air) of 250 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find the ground speed of the plane. Round the result to the nearest hundredth.Explanation / Answer
A vector represents the direction N450W and the magnitude 80 is (80 sin 450 ; 80 cos 45 0 ).
A vector represents the direction N600E and the magnitude 250 is (250 sin 600 ; 250 cos 600 )
Components N have the same directions so they will add.
Component N-S
y=250 sin 600+80 sin 450= 273
Component E-W
x=250 cos 600-80 cos 45 0=68.43
Direction is :
fi = arc tan y/x = tan-1(273/68.43) = 75.920
Magnitude
IvI=sqrt(x^2+y^2) = sqrt(68.432+2732) = 281.445
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