+0/2 ET2 10.2.026 My Notes Ask Your T The magnitude of a velocity vector is call

Question

+0/2 ET2 10.2.026 My Notes Ask Your T The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45'W at a speed of 50 km/h. (This means that the direction from which the wind blows is 45 west of the northerly direction.) A pilot is steering a plane in the direction N60 E at an airspeed (speed in still air) of 150 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 true course and the ground speed of the plane. (Round your answers to one decimal place.) true course N ground speed X km/h Need Help?ReadtChat About t

Explanation / Answer

here

the first vecot is in the direction N45W and magnitude is = -50 * sin45deg , 50 * cos45deg

the secnond vector is in the direction N60E and the magnitude is = 150*sin60deg , 150*cos60deg

the true course is ( -50 * sin(45deg) + 150 * sin60deg , 50*cos(45deg) + 150*cos(60deg))

so ,

( 75*sqrt(3) - 25*sqrt(2) , 75 + 25*sqrt(2))

then the angle (theta) = tan^-1((75 + 25*sqrt(2)) / (75 * sqrt(3) - 25*sqrt(2)))

theta = 49.41 deg

so the direction is E49.41degN

then the ground speed is = sqrt(( 75*sqrt(3) - 25 *sqrt(2))^2 + (75 + 25*sqrt(2))^2

ground speed = 145.3 km/h

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