Velocities Have Both Direction and Magnitude and Thus Are Vectors $\mathrm { N } \mathrm {} 60 ^ { \circ } \mathrm { W }$

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 $\mathrm { N } \mathrm {} 60 ^ { \circ } \mathrm { W }$ at a speed of 80 $\mathrm { km } / \mathrm { h }$ . (This means that the direction from which the wind blows is $60 ^ { \circ }$ west of the northerly direction.) A pilot is steering a plane in the direction $\mathrm { N } \mathrm {} 45 ^ { \circ } \mathrm { E }$ at an airspeed (speed in still air) of $250 \mathrm {~km} / \mathrm { h }$ . 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.