Question

1. Камень бросили вертикально вверх на высоту h0 = 10 м. Через какое время t он упадет на землю? На какую высоту поднимется камень, если начальную скорость камня увеличить вдвое?

Answer 1

h = v^2 /2g

t = 2tподъема = 2v/g = 2кор(2h/g) = 2,8 c

Если скорость выброса увеличить вдвое, то высота увеличится вчетверо.

h1 = 40 м.

Ответ: 2,8 с;  40 м.

Answer 2

Время подъема тела находится по формуле tп = v/g

Высота подъема определяется по формуле h = v²/(2g)

                                                                  v² = 2gh

                                                                  v = √(2gh)

tп = √(2gh)/g

tп = √(2·10·10)/10 = √2 ≈ 1,4 (c)

t = 2tп = 2·1,4 = 2,8 (с)

Если скорость увеличится в 2 раза, время подъема также увеличится в 2 раза. Следовательно, высота подъема увеличится в 4 раза, т.е., будет равна 40 м.

Ответ. t=2,8 с; h=40 м.

Answer 3

Problem Analysis

We are given the initial height of a stone thrown vertically upward, and we need to find the time it takes for the stone to fall back to the ground and the height it reaches if the initial velocity is doubled.

Solution

To find the time it takes for the stone to fall back to the ground, we can use the equation of motion for free fall:

h = h0 + v0t - (1/2)gt^2

where: - h is the final height (0 in this case, as the stone falls back to the ground) - h0 is the initial height (10 m in this case) - v0 is the initial velocity (which we need to find) - t is the time it takes for the stone to fall back to the ground - g is the acceleration due to gravity (approximately 9.8 m/s^2)

We can rearrange the equation to solve for t:

0 = h0 + v0t - (1/2)gt^2

0 = 10 + v0t - (1/2)(9.8)t^2

0 = 10 + v0t - 4.9t^2

Since the stone is thrown vertically upward, the initial velocity is in the opposite direction of gravity. Therefore, we can take the initial velocity as negative.

Now, let's solve for t:

0 = 10 - v0t - 4.9t^2

v0t = 10 - 4.9t^2

v0 = (10 - 4.9t^2) / t

To find the time it takes for the stone to fall back to the ground, we need to solve this equation. However, we don't have enough information to determine the value of t.

Now, let's consider the second part of the question. If we double the initial velocity of the stone, we can find the new height it reaches. Let's denote the new height as h1.

Using the equation of motion for free fall, we can write:

h1 = h0 + (2v0)t - (1/2)gt^2

Substituting the value of h0 = 10 m and v0 = 2v0 (doubled initial velocity), we get:

h1 = 10 + (2v0)t - (1/2)gt^2

We can see that the new height h1 will be greater than the initial height h0.

Unfortunately, we don't have enough information to calculate the exact value of h1 without knowing the time t.

In summary, we can find the time it takes for the stone to fall back to the ground using the equation 0 = 10 - v0t - 4.9t^2, but we need more information to solve for t. Additionally, we can determine the new height h1 if we know the time t, but again, we need more information to calculate it.

Please provide additional information if available, so we can provide a more accurate answer.