An airplane is flying due west at a velocity of 100 m/s. The wind is blowing south at 5 m/s.
a. Draw a labeled diagram of the situation.
b. Find the resulting ground speed and bearing of the airplane?
gjjrtj
Stocazzo
What are the plane's actual speed and direction angle?
a. To draw a labeled diagram of the situation, you can draw a coordinate system with the x-axis representing the east-west direction and the y-axis representing the north-south direction. Label the west direction as positive x and the south direction as negative y. Place an airplane symbol on the origin point, representing the initial position of the airplane. Draw an arrow pointing due west with a length of 100 units to represent the velocity of the airplane. Draw another arrow pointing due south with a length of 5 units to represent the velocity of the wind. Label the vectors with their respective magnitudes.
b. To find the resulting ground speed and bearing of the airplane, we can use vector addition. Since the airplane is flying due west and the wind is blowing due south, the resulting velocity (relative to the ground) will be the vector sum of these two velocities.
To find the ground speed, we can use the Pythagorean theorem. The magnitude of the resulting velocity is given by:
Resulting velocity magnitude = sqrt((100^2) + (5^2))
= sqrt(10000 + 25)
= sqrt(10025) m/s
The bearing of the airplane is given by the angle formed between its resulting velocity and the positive x-axis. To find this angle, we can use trigonometry. The angle is given by:
Angle = atan(5 / 100)
= atan(0.05)
= 2.862 degrees (rounded to 3 decimal places)
Therefore, the resulting ground speed is approximately sqrt(10025) m/s, and the bearing of the airplane is approximately 2.862 degrees.