Question

For altitudes up to 36,000 feet, the relationship between ground temperature and atmospheric temperature can be described by the formula t=−0.0035a+g. Determine the altitude in feet when t is -61.2 °F and g is 20 °F.

a. 11,542 feet.
b. 18,571 feet.
c. 23,429 feet.
d. 29,857 feet.

Answer 1

By substituting the atmospheric temperature (-61.2 °F) and ground temperature (20 °F) into the formula and solving for altitude, we find that the closest altitude is approximately 23,200 feet, corresponding to option (c) 23,429 feet.

Step-by-step explanation:

To find the altitude where the atmospheric temperature is -61.2 °F when the ground temperature is 20 °F, we use the given formula: t = -0.0035a + g. Here, t is the atmospheric temperature, a is the altitude in feet, and g is the ground temperature.

• Insert the known values into the equation: -61.2 = -0.0035a + 20.
• Subtract 20 from both sides to isolate the terms with a: -61.2 - 20 = -0.0035a, which simplifies to -81.2 = -0.0035a.
• Divide both sides by -0.0035 to solve for a: a = -81.2 / -0.0035.
• Calculating the above expression provides us the altitude a: a ≈ 23,200 feet.

Therefore, the correct option is (c) 23,429 feet, since 23,200 feet is closest to this choice when rounding to the nearest options provided.