The magnitude of a velocity vector is called speed . Suppose that a wind is blow

Question

The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45°W at a speed of 60 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 300 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.)

Explanation / Answer

First brake you vector into its cardinal directions speeds
Using your meaning to the wind directions
N45°W 50 km/h is the hypotenuse is 50. it's is Adjacent 252 km/h N and an Opposite of - 252 km/h E (aka west) (being 45-45-90 triangle)

N60°E 200 km/h is the hypotenuse is 200 it's it's Adjacent is 100 km/h N and an Opposite of 1003 km/h E (aka west) (being 30-60-90 triangle)

Now add the Adjacent together 100 + 252 = 25(4+2) km/h N
and the Opposites 1003 - 252 = -25 (2 -43) km/h E (aka west)

Now us Pythagoras' theorem c² = a² + b² to find the magnitude of the resulting vector.
(25(4+2))² + (-25 (2 -43))² = c²
625(4+2)² + 625 (2 -43)² = c²
c193.193 km/h

Tan t = o/a = 25(4+2)/(-25 (2 -43)
t = 44.48°
so the true course is 193.193 km/h N44.48°W

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