All angles are CCW from +x-axis.
Vp + Vw = 420km/h[97o].
420[90o] + Vw[225o] = 420[97o]
420i + Vw*Cos225+Vw*sin225 = 420*Cos97 +420*sin97 = 420i - 0.707Vw - i0.707Vw = -51.2 + 417i = -51.2 -3i.
0.707Vw (-1-1i) = -51.2 - 3i.
0.707Vw(1.41[225o]) = 51.3[183.4o].
Vw[225o] = 51.3[183.4o]
Vw = 51.3km/h[-41.6]
Speed of wind = 51.3km/h.
A plane head north with an airspeed of 420 km/h. However, relative to the ground, it travels in a direction 7.0 west of north. if the wind's direction is towards the southwest (45.0 south of west), what is the wind speed?
2 answers
vector diagram would be the 420 heading north + unknown head NW = unknown heading 7 degrees W of N
7 degrees in bottom corner 45 + 90= 135 above that and 180-7-135 = 38 in the top left corner
using sine law Vw/sin(7)= 420/sin(38) where Vw = velocity of wind = 83km/hr
7 degrees in bottom corner 45 + 90= 135 above that and 180-7-135 = 38 in the top left corner
using sine law Vw/sin(7)= 420/sin(38) where Vw = velocity of wind = 83km/hr