When an airplane leaves the runway, its angle of elevation is 18 and its speed is 275 feet per second. Find the airplane’s altitude after one minute (60 seconds). Assume a constant angle of elevation. Draw the scenario, if you can.
To find the airplane's altitude after one minute, we first need to find the horizontal distance it travels in one minute. We can do this by using the speed and time given.
Given:
Angle of Elevation = 18 degrees
Speed = 275 feet per second
Time = 60 seconds
To find the horizontal distance, we can use the trigonometric relation between the angle of elevation and the horizontal distance (also known as the cosine function).
cos(angle) = adjacent/hypotenuse
In this case, the adjacent side represents the horizontal distance (d) and the hypotenuse represents the speed (275 feet per second).
cos(18 degrees) = d/275
Now, let's solve for d:
d = 275 * cos(18 degrees)
Using a calculator or a trigonometric table, we find that cos(18 degrees) is approximately 0.951.
d ≈ 275 * 0.951
d ≈ 261.83 feet
So, the airplane travels approximately 261.83 feet horizontally in one minute.
To find the altitude, we need to find the vertical distance traveled by the airplane in one minute. We can use the angle of elevation and the formula for calculating the altitude:
altitude = horizontal distance * tan(angle)
altitude = 261.83 * tan(18 degrees)
Again, using a calculator or a trigonometric table, we find that tan(18 degrees) is approximately 0.3249.
altitude ≈ 261.83 * 0.3249
altitude ≈ 85.06 feet
Therefore, the airplane's altitude after one minute is approximately 85.06 feet.
As for the scenario, I apologize, but as a text-based AI, I am unable to draw diagrams. However, you can visualize the scenario by picturing an airplane taking off from the runway and ascending at an angle of 18 degrees from the horizontal.