The problem involves finding the speed of an airplane based on the change in angle of elevation and the time it takes for the change to occur. Let's break down the problem into smaller steps.

1. Understanding the problem:
- The angle of elevation is the angle between the horizontal line and the line of sight from an observer on the ground to an object.
- In this case, the initial angle of elevation is 60° and the final angle of elevation is 30°.
- The airplane maintains a constant height of 3000√3m throughout the flight.
- We need to find the speed of the airplane.

2. Drawing a diagram:
- Draw a diagram with a horizontal line representing the ground and a vertical line representing the height of the airplane.
- Mark a point on the ground where the observer is located.
- Draw a line from the observer to the airplane, making an angle of 60° with the horizontal line.
- After the flight, draw another line from the observer to the airplane, making an angle of 30° with the horizontal line.
- Label the distance between the observer and the airplane as 'x' (which we need to find) and the constant height of the airplane as 3000√3m.

3. Applying trigonometry:
- In the initial position, the tangent of the angle of elevation can be expressed as tan(60°) = (3000√3) / x.
- In the final position, the tangent of the angle of elevation can be expressed as tan(30°) = (3000√3) / (x + 30).

4. Solving the equations:
- Using the tangent values for 60° and 30°, we can rewrite the equations as:
√3 = (3000√3) / x
1/√3 = (3000√3) / (x + 30)
- Cross-multiplying, we get:
x = 3000
x + 30 = 9000√3

5. Finding the speed of the airplane:
- The speed of the airplane can be calculated by dividing the distance traveled (x) by the time taken (30 seconds).
- The speed of the airplane is: 3000 / 30 = 100 m/s.

Therefore, the speed of the airplane is 100 m/s.

no