7. An aircraft flies at 720 km/h in a direction 40° south of west. A strong wind is blowing at 85 km/h in a direction 35° east of south. Calculate: 7.1 The resultant velocity of the aircraft.
To find the resultant velocity of the aircraft, we must first break down the velocity of the aircraft and the velocity of the wind into their horizontal and vertical components.
Velocity of the aircraft:
Speed = 720 km/h
Direction = 40° south of west
Horizontal component of the velocity of the aircraft:
720 km/h * cos(40°) = 548.381 km/h westward
Vertical component of the velocity of the aircraft:
720 km/h * sin(40°) = 466.369 km/h southward
Velocity of the wind:
Speed = 85 km/h
Direction = 35° east of south
Horizontal component of the velocity of the wind:
85 km/h * cos(35°) = 69.843 km/h eastward
Vertical component of the velocity of the wind:
85 km/h * sin(35°) = 48.939 km/h southward
Now we add up the horizontal and vertical components of the aircraft's velocity and wind velocity to find the resultant velocity:
Horizontal component: 548.381 km/h (aircraft) - 69.843 km/h
Vertical component: 466.369 km/h (aircraft) - 48.939 km/h
Resultant velocity (magnitude):
√[(478.538)^2 + 417.430^2]
= √[228553 + 174304]
= √402857
= 634.57 km/h
Therefore, the resultant velocity of the aircraft is 634.57 km/h.