Question

Біля підніжжя гори барометр показує 740 мм рт. ст., а на вершині 683 мм рт. ст. Чому дорівнює висота гори?​

Answer 1

На 100 м приходится 12.5 мм ст столба

740-683 = 57 мм рт столба

57:12.5= 4.6

высота 460 м

вроде бы так

Answer 2

Understanding the Problem

The problem states that the barometer shows a reading of 740 mmHg at the base of the mountain and a reading of 683 mmHg at the summit. We need to determine the height of the mountain based on this information.

Barometric Pressure and Altitude

Barometric pressure is the pressure exerted by the atmosphere at a particular location. It decreases as altitude increases because there is less air above to exert pressure. This relationship between barometric pressure and altitude is known as the barometric formula.

The Barometric Formula

The barometric formula describes the relationship between barometric pressure and altitude. It states that the pressure at a given altitude is equal to the pressure at sea level multiplied by the exponential of the negative ratio of the altitude to the scale height.

Calculating the Height of the Mountain

To calculate the height of the mountain, we can use the barometric formula. We have the pressure at the base of the mountain (740 mmHg) and the pressure at the summit (683 mmHg). We can assume that the pressure at sea level is approximately 760 mmHg.

Using the barometric formula, we can set up the following equation:

P1/P2 = e^(-h/H)

Where: - P1 is the pressure at the base of the mountain (740 mmHg) - P2 is the pressure at the summit (683 mmHg) - h is the height of the mountain (what we want to find) - H is the scale height (a constant that depends on the temperature and composition of the atmosphere)

By rearranging the equation, we can solve for h:

h = -H * ln(P2/P1)

Calculating the Height

To calculate the height, we need to know the value of the scale height (H). The scale height is the vertical distance over which the pressure decreases by a factor of e (approximately 2.71828) due to the exponential term in the barometric formula.

The scale height varies depending on the temperature and composition of the atmosphere. The average scale height for Earth's atmosphere is approximately 8.5 kilometers (8,500 meters).

Using the given values, we can calculate the height of the mountain as follows:

h = -8500 * ln(683/740)

Calculating this expression gives us the height of the mountain.

Conclusion

To determine the height of the mountain based on the given barometric pressure readings, we can use the barometric formula. By plugging in the values of the pressure at the base and summit of the mountain, as well as the average scale height, we can calculate the height of the mountain.