At an airport, a flight controller is in a tower 45m above the ground. She observes an airplane flying at a constant altitude at an angle of elevation of 14 degrees from her line of sight. Seven seconds later, the airplane flies directly overhead.
If the airplane has a constant speed of 370 KM/H, what distance, in meters, did it cover between the time the flight controller first observed the airplane to when it passed overhead?"
First convert 370 km/h to 102.8 m/s.
Multiply that by 7 seconds for the answer, 719 m. You don't need the initial elevation angle nor the tower height.
To solve this problem, we can first calculate the distance traveled by the airplane horizontally from the time the flight controller first observed it until it passed overhead. We can then use this distance, along with the angle of elevation and the flight controller's height, to calculate the total distance traveled by the airplane.
Step 1: Calculate the horizontal distance traveled by the airplane.
The speed of the airplane is given in kilometers per hour, but we need to convert it to meters per second, as the time given is in seconds.
370 km/h = 370,000 m/3600 s = 102.78 m/s
The time it takes for the airplane to cross directly overhead is given as 7 seconds. Therefore, the horizontal distance it travels can be calculated as:
Distance = Speed x Time
Distance = 102.78 m/s x 7 s
Distance = 719.46 m
So, the airplane travels 719.46 meters horizontally during the 7 seconds.
Step 2: Calculate the total distance traveled by the airplane.
To find the total distance, we need to consider the vertical distance as well. The vertical distance can be calculated using the height of the flight controller and the angle of elevation.
In the given problem, the flight controller is 45 meters above the ground, and the angle of elevation is given as 14 degrees. We can use basic trigonometry to find the vertical distance.
Vertical Distance = Height of Flight Controller x tan(Angle of Elevation)
Vertical Distance = 45 m x tan(14 degrees)
Vertical Distance ≈ 11.61 m
The total distance traveled by the airplane is the sum of the horizontal and vertical distances. Therefore, the total distance is:
Total Distance = Horizontal Distance + Vertical Distance
Total Distance = 719.46 m + 11.61 m
Total Distance ≈ 731.07 meters
So, the airplane covered a distance of approximately 731.07 meters from the time the flight controller first observed it until it passed overhead.