An Airplane Descent Calculation: Determine the New Altitude
What is the new altitude after 10 minutes of descent for an airplane traveling at 500 mph at a cruising altitude of 6.5 mi with a 30-degree angle of descent from the horizontal?
The new altitude after 10 minutes of descent will be approximately 5.5 miles.
Calculation Explanation:
Given that the angle of descent is 30 degrees, we can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side represents the change in altitude, and the adjacent side is the horizontal distance traveled by the airplane in 10 minutes.
Firstly, we need to calculate the horizontal distance traveled by the airplane in 10 minutes. This can be found by multiplying the speed of the airplane (500 mph) by the time (10 minutes) and converting the time to hours for consistency:
Horizontal Distance = Speed x Time = 500 mph x (10 minutes / 60 minutes) = 83.33 miles
Next, utilizing the tangent function with the given 30-degree angle:
tan(30 degrees) = Opposite / Adjacent
tan(30 degrees) = Change in Altitude / 83.33 miles
Change in Altitude ≈ tan(30 degrees) x 83.33 miles
Change in Altitude ≈ 0.5774 x 83.33 miles ≈ 48.11 miles
Adding this change in altitude to the initial altitude of 6.5 miles gives us the new altitude:
New Altitude ≈ 6.5 miles + 48.11 miles ≈ 54.61 miles
Rounded to the nearest tenth of a mile, the new altitude after 10 minutes of descent will be approximately 5.5 miles.