Question

Камень, брошенный почти вертикально вверх с поверхности земли, через 3 после броска упал на крышу дома высотой 15 см. Найдите начальную скорость камня. Сопротивление воздуха не учитывается.​

Answer 1

Ответ:

Начальная скорость камня равна 14,75 м/с.

Объяснение:

Дано:

t = 3с

h = 15 см = 0,15 м

g = 9,8 м/с²

Найти:

v₀ - ?

Решение:

$\large \boldsymbol {} h = v_{0} t - \frac{gt^{2} }{2}$, где

h - высота (м)

v₀ - начальная скорость (м/с)

t - время (с)

g - ускорение свободного падения (≈9,8 м/с²).

Выразим начальную скорость:

$\large \boldsymbol {} v_{0} = \frac{h + \frac{gt^{2} }{2} }{t}$

$v_{0} = \frac{0,15 + \frac{9,8 * 3^{2} }{2} }{3} = \frac{0,15 + 44,1}{3} = \frac{44,25}{3} = 14,75 \ m/s$

Answer 2

Problem Analysis

We are given the following information: - A stone is thrown almost vertically upwards from the surface of the Earth. - After 3 seconds, the stone falls and lands on the roof of a house, which is 15 cm high. - We need to find the initial velocity of the stone.

To solve this problem, we can use the equations of motion under constant acceleration.

Solution

Let's assume the initial velocity of the stone is v₀ and the acceleration due to gravity is g (approximately 9.8 m/s²).

Using the equation of motion for vertical motion:

h = v₀t - (1/2)gt²

where: - h is the height of the roof (15 cm = 0.15 m) - t is the time taken (3 seconds) - g is the acceleration due to gravity (9.8 m/s²)

Substituting the given values into the equation, we can solve for v₀.

Calculation

Let's calculate the initial velocity v₀ using the equation of motion:

h = v₀t - (1/2)gt²

Substituting the given values: - h = 0.15 m - t = 3 s - g = 9.8 m/s²

We can rearrange the equation to solve for v₀:

v₀ = (h + (1/2)gt²) / t

Substituting the values and calculating:

v₀ = (0.15 + (1/2) * 9.8 * 3²) / 3

v₀ = (0.15 + 44.1) / 3

v₀ = 44.25 / 3

v₀ ≈ 14.75 m/s

Answer

The initial velocity of the stone is approximately 14.75 m/s.

Conclusion

In this problem, we used the equation of motion for vertical motion to find the initial velocity of a stone thrown almost vertically upwards. The stone fell and landed on the roof of a house after 3 seconds. By substituting the given values into the equation, we found that the initial velocity of the stone is approximately 14.75 m/s.