Determining New Altitude of Airplane after Descent

What is the new altitude of an airplane traveling at 600 mph at a cruising altitude of 6.6 mi, beginning its descent at a 3° angle, after 10 minutes?

The new altitude is approximately 6.3 miles.

Calculating New Altitude of Airplane

Final Answer: To find the new altitude of the airplane after 10 minutes of descent at a 3° angle, we can use trigonometry. The change in altitude can be calculated using the sine function and the ground distance covered in 10 minutes can be found using the formula speed = distance/time. By plugging in the values, we can determine that the new altitude is approximately 6.3 miles.

Explanation:

To find the new altitude of the airplane: we can use trigonometry. Since the angle of descent is 3° from the horizontal, we can use the sine function to calculate the change in altitude. The formula is sin(angle) = opposite/hypotenuse. In this case, the opposite side is the change in altitude and the hypotenuse is the ground distance covered in 10 minutes. The ground distance covered in 10 minutes: can be calculated using the formula speed = distance/time. Rearranging the formula, we have distance = speed x time. Plugging in the values, distance = 600 mph x 10 min = 6000 miles. Calculating the change in altitude: using the sine function: sin(3°) = change in altitude/6000 miles. Rearranging the formula, we have change in altitude = 6000 miles x sin(3°). Using a calculator, sin(3°) is approximately 0.0524. So, the change in altitude is approximately 6000 miles x 0.0524 = 314.4 miles. Therefore, the new altitude after 10 minutes is approximately 6.6 mi - 314.4 mi = 6.3 miles (rounded to the nearest tenth of a mile).
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