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 can treat the aircraft's velocity and the wind's velocity as vectors and calculate their sum.
Let's break down the aircraft's velocity into its horizontal and vertical components:
Horizontal component = 720 km/h * cos(40°) = 720 km/h * cos(40°) ≈ 550.93 km/h
Vertical component = 720 km/h * sin(40°) = 720 km/h * sin(40°) ≈ 462.72 km/h
Now, let's break down the wind's velocity into its horizontal and vertical components:
Horizontal component = 85 km/h * cos(35°) = 85 km/h * cos(35°) ≈ 69.58 km/h
Vertical component = 85 km/h * sin(35°) = 85 km/h * sin(35°) ≈ 48.86 km/h
The resultant horizontal component = horizontal component of aircraft + horizontal component of wind
= 550.93 km/h + 69.58 km/h = 620.51 km/h
The resultant vertical component = vertical component of aircraft + vertical component of wind
= 462.72 km/h + 48.86 km/h = 511.58 km/h
Now, let's find the magnitude and direction of the resultant velocity:
Resultant velocity = sqrt((620.51 km/h)^2 + (511.58 km/h)^2) ≈ 797.68 km/h
Angle = tan^(-1) (511.58/620.51) ≈ 38.35°
Therefore, the resultant velocity of the aircraft is approximately 797.68 km/h in a direction 38.35° south of west.