Question

At a height of h meters, you can see V kilometers to the horizon. These numbers are related by the equation V=3.5√h. A person can see 392 km to the horizon from an airplane window. How high is the airplane? (How many meters high?)

Answer 1

To determine the height of the airplane, we use the formula V = 3.5√h with V = 392 km. By isolating h and solving the equation, we find that the height h is approximately 12,544 meters.

Step-by-step explanation:

A student has a question regarding the relationship between the altitude from which they observe the horizon and the distance to the horizon. They've been provided with an equation V = 3.5√h, where V is the distance to the horizon in kilometers and h is the height above sea level in meters. The student shared that a person can see 392 km to the horizon from an airplane window and wishes to calculate how high the airplane is in meters.

Step-by-step Solution

1. First, write down the given equation: V = 3.5√h.
2. Substitute the value for V given in the problem (392 km) into the equation: 392 = 3.5√h.
3. To solve for h, we need to isolate h on one side. We do this by squaring both sides of the equation to remove the square root: (392 / 3.5)^2 = h.
4. Perform the calculations to find the value of h.

By doing the arithmetic, we find:

• (392 / 3.5)^2 = (112)^2
• h = 12544 meters

Therefore, the airplane is approximately 12,544 meters high.