Question

Камень массой 200 г свободно падает без начальной скорости с высоты 20 м. Через какое время камень упадет на землю? Сопротивлением воздуха пренебречь.

Answer 1

Ответ:

2 секунды

Объяснение:

Формула времени падения тела без начальной скорости:

$\sqrt{\frac{2h}{g} }$ (выводится из формулы h = $\frac{gt^2}{2}$)

Подставляем:

t = $\sqrt{\frac{2 * 20}{10} } = \sqrt{\frac{40}{10} } = \sqrt{4} = 2$ секунды

Answer 2

Problem Analysis

We are given that a stone with a mass of 200 g is freely falling from a height of 20 m without any initial velocity. We need to find the time it takes for the stone to fall to the ground, neglecting air resistance.

Solution

To solve this problem, we can use the equations of motion for free fall. The equation that relates the distance fallen, initial velocity, time, and acceleration due to gravity is:

d = ut + (1/2)gt^2

Where: - d is the distance fallen (20 m in this case) - u is the initial velocity (0 m/s in this case) - g is the acceleration due to gravity (approximately 9.8 m/s^2)

We can rearrange this equation to solve for time (t):

t = sqrt(2d/g)

Let's substitute the given values into the equation to find the time it takes for the stone to fall to the ground.

Calculation

Using the equation t = sqrt(2d/g), where d = 20 m and g = 9.8 m/s^2:

t = sqrt(2 * 20 / 9.8) t ≈ sqrt(40 / 9.8) t ≈ sqrt(4.08) t ≈ 2.02 seconds

Therefore, the stone will take approximately 2.02 seconds to fall to the ground.

Answer

The stone will take approximately 2.02 seconds to fall to the ground.