What is the ground velocity of an airplane
if its air velocity is 800 km/h [E] and the
wind velocity is 60 km/h [42� E of N]?
To find the ground velocity of an airplane, you need to consider the effect of the wind on its motion.
Step 1: Convert the given velocities to vector form.
Air velocity = 800 km/h [E]
Wind velocity = 60 km/h [42 E of N]
Step 2: Resolve the wind velocity into its east (x) and north (y) components.
Wind velocity (x-component) = 60 km/h * cos(42°)
Wind velocity (y-component) = 60 km/h * sin(42°)
Step 3: Add the x-component of the wind velocity to the x-component of the air velocity to get the ground velocity in the east direction.
Ground velocity (x) = 800 km/h + Wind velocity (x-component)
Step 4: Add the y-component of the wind velocity to the y-component of the air velocity to get the ground velocity in the north direction.
Ground velocity (y) = Wind velocity (y-component)
Step 5: Use the Pythagorean theorem to find the magnitude of the ground velocity.
Ground velocity (magnitude) = sqrt((Ground velocity (x))^2 + (Ground velocity (y))^2)
Step 6: Find the direction of the ground velocity.
Ground velocity (direction) = arctan(Ground velocity (y) / Ground velocity (x))
By following these steps and plugging the given values into the calculations, you can determine the ground velocity of the airplane.
To find the ground velocity of an airplane, you need to consider both its air velocity and the wind velocity. The ground velocity is the combination of these two velocities.
In this case, the air velocity of the airplane is given as 800 km/h towards the east (E). The wind velocity is given as 60 km/h towards the northeast (42° east of north).
To find the ground velocity, we'll break down the vectors into their respective components. Let's assume that the positive x-axis represents the east direction, and the positive y-axis represents the north direction.
The air velocity towards the east gives us a component of 800 km/h in the positive x-direction (Vx_air = +800 km/h) and no component in the y-direction (Vy_air = 0 km/h).
The wind velocity towards the northeast can be broken down into two components: one in the positive x-direction and one in the positive y-direction. We can calculate these components using trigonometry.
The angle of 42° east of north means that we need to subtract 42° from 90° (which represents the north direction) to get the angle relative to positive x-axis. So, the angle relative to the positive x-direction is 90° - 42° = 48°.
Using trigonometry, we can calculate the x-component (Vx_wind) and y-component (Vy_wind) of the wind velocity:
Vx_wind = 60 km/h * cos(48°)
Vy_wind = 60 km/h * sin(48°)
Now we can calculate the ground velocity by adding up the individual components:
Vx_ground = Vx_air + Vx_wind
Vy_ground = Vy_air + Vy_wind
Finally, we can find the magnitude and direction of the ground velocity using the Pythagorean theorem and trigonometry:
Magnitude of the ground velocity (V_ground) = sqrt(Vx_ground^2 + Vy_ground^2)
Direction of the ground velocity = atan(Vy_ground / Vx_ground)
By substituting the values into the equations, you can compute the magnitude and direction of the ground velocity.