Question

На какой высоте ускорение свободного падения на 75% меньше, чем на земле

Answer 1

Ответ:

1/3 g = G * M / (R + h)²; g — ускорение свободного падения на поверхности Земли (const, g = 9,81 м/с2), G — гравитационная постоянная (const, G = 6,67 * 10-11 м³/ (кг*с²)), M — масса Земли (const, М = 5,97 * 1024 кг), R — радиус Земли (const, R = 6371000 м), h — высота над.

Объяснение:

Answer 2

Height at which acceleration due to gravity is 75% less than on Earth

The height at which the acceleration due to gravity is 75% less than on Earth can be calculated using the formula for acceleration due to gravity, which is given by:

g' = g / (1 + h/R)^2

Where: - g' = acceleration due to gravity at height h - g = acceleration due to gravity on the surface of the Earth - h = height above the surface of the Earth - R = radius of the Earth

To find the height at which the acceleration due to gravity is 75% less than on Earth, we can use the given percentage decrease and solve for h.

Using the formula, we can calculate the height at which the acceleration due to gravity is 75% less than on Earth.

Calculations: Given that the acceleration due to gravity on Earth is approximately 9.8 m/s^2, we can use this value in the formula to find the height.

g' = 9.8 / (1 + h/R)^2

We need to solve for h when g' = 0.25g (75% less than g).

0.25g = 9.8 / (1 + h/R)^2

Solving for h: 1 + h/R = √(9.8 / 0.25g) h/R = (√(9.8 / 0.25g)) - 1 h = R * ((√(9.8 / 0.25g)) - 1)

Using the value of the radius of the Earth (approximately 6371 km or 6,371,000 meters) and the acceleration due to gravity on Earth (9.8 m/s^2), we can calculate the height h.

h ≈ 3.1 * 10^6 meters

Therefore, the height at which the acceleration due to gravity is 75% less than on Earth is approximately 3.1 million meters.

(#1)