an airplane is flying at 550 km/h on a heading of 080. the wind is blowing at 60 km/h from a bearing of 120. Find the ground velocity of the airplane.

Please Help! Thanks in advance.

To find the ground velocity of the airplane, we need to consider both the velocity of the airplane and the velocity of the wind.

Let's break down the given information:

- Airplane's velocity: 550 km/h
- Heading: 080

- Wind velocity: 60 km/h
- Bearing: 120

First, we need to convert the heading and bearing angles to compass headings. The compass headings range from 0° (north) to 360° (north again).

Given that the heading is 080, we can directly convert it to a compass heading.

Heading: 080°

Now, let's convert the bearing from 120 to a compass heading.

Bearing: 120°
Compass Heading: (360° - Bearing) = (360° - 120°) = 240°

Now, we need to resolve the vectors for the airplane's velocity and the wind's velocity.

- Airplane's velocity:
- Speed: 550 km/h
- Heading: 080°

To resolve the airplane's velocity into horizontal (E/W) and vertical (N/S) components, we use trigonometry.

- Horizontal component (E/W):
- Speed * cos(heading)
- 550 km/h * cos(80°)

- Vertical component (N/S):
- Speed * sin(heading)
- 550 km/h * sin(80°)

- Wind's velocity:
- Speed: 60 km/h
- Heading: 240°

Similarly, we resolve the wind's velocity into horizontal (E/W) and vertical (N/S) components.

- Horizontal component (E/W):
- Speed * cos(heading)
- 60 km/h * cos(240°)

- Vertical component (N/S):
- Speed * sin(heading)
- 60 km/h * sin(240°)

Now, we add the resolved horizontal and vertical components of both the airplane's velocity and the wind's velocity to get the ground velocity.

- Horizontal component of airplane's velocity + Horizontal component of wind's velocity = East/West component of ground velocity
- Vertical component of airplane's velocity + Vertical component of wind's velocity = North/South component of ground velocity

Finally, we calculate the magnitude (speed) and direction of the ground velocity vector using the Pythagorean theorem and trigonometry.

- Ground velocity (speed):
- sqrt((East/West component of ground velocity)^2 + (North/South component of ground velocity)^2)

- Ground velocity (direction):
- arctan((North/South component of ground velocity) / (East/West component of ground velocity))

By plugging in the values and performing the calculations, you should be able to find the ground velocity of the airplane.

Vp = (550km/h,80deg) + (60km/h,120dg).

X = hor = 550cos80 + 60cos120,
X = 95.51 + (-30) = 65.51km/h.

Y = ver = 550sin80 + 60sin120,
Y = 541.6 + 51.96 = 593.6km/h.

Vp^2=(65.51)^2 + ((593.6)^2=356,652.5,
Vp = 597.2km/h = Speed of plane.