At an airport, a flight controller was in a tower 40m above the ground. When she first observed a plane it was at an angle of elevation of 12 (degrees) from her line of sight and flying at a constant altitude (height)
The plane had a constant speed of 360km/h
Eight seconds later the plane flew directly overhead.
On reaching the tower, the plane climbed for the next 15 seconds, without changing speed, to reach a new altitude of 1500 meters above the ground.
What was the plane's angle of ascent during this time?
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To find the plane's angle of ascent, we need to calculate the change in altitude and the corresponding change in time. Then, we can use trigonometry to determine the angle.
First, let's find the change in altitude. The plane climbed from a height of 40m above the ground to a new altitude of 1500m above the ground. Therefore, the change in altitude is:
1500m - 40m = 1460m
Next, we need to calculate the corresponding change in time. We know that the plane flew directly overhead 8 seconds after the flight controller observed it. Therefore, the total time it took for the plane to climb is:
8s + 15s = 23s
Now that we have the change in altitude and the corresponding change in time, we can use trigonometry to find the angle of ascent.
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the change in altitude (1460m) and the adjacent side is the change in time (23s). Therefore, the tangent of the angle of ascent is:
tan(angle) = 1460m / 23s
To find the angle, we can take the inverse tangent (arctan) of both sides:
angle = arctan(1460m / 23s)
Using a calculator, we find that angle =~ 61.3 degrees.
So, the plane's angle of ascent during this time is approximately 61.3 degrees.