Question

Камень бросили вертикально вниз с высоты 27м со скоростью 2м/с. Через какое время он упадёт на землю? С какой скоростью?

Answer 1

S=27 м
V= 2 м/с
t - ?
V-?
Решение:
Камень будет падать со скоростью 2 м/с.
t=S:V
t=27 м: 2 м/с=13,5 с
Ответ: t= 13.5 с.

Answer 2

Problem Analysis

We are given the following information: - A stone is thrown vertically downward from a height of 27m. - The initial velocity of the stone is 2m/s.

We need to find: 1. The time it takes for the stone to fall to the ground. 2. The final velocity of the stone when it hits the ground.

Solution

To solve this problem, we can use the equations of motion for uniformly accelerated motion. Since the stone is thrown vertically downward, we can assume that the acceleration due to gravity is acting in the downward direction.

Let's break down the problem into two parts: finding the time it takes for the stone to fall and finding the final velocity of the stone.

Time to Fall

We can use the equation h = ut + (1/2)gt^2, where: - h is the height from which the stone is thrown (27m), - u is the initial velocity of the stone (-2m/s, negative because it is thrown downward), - g is the acceleration due to gravity (-9.8m/s^2, negative because it acts in the opposite direction of the initial velocity), - t is the time taken for the stone to fall.

Simplifying the equation, we get: 27 = -2t + (1/2)(-9.8)t^2

To solve this quadratic equation, we can use the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a)

Comparing the equation with the standard quadratic equation form ax^2 + bx + c = 0, we have: - a = (1/2)(-9.8) = -4.9 - b = -2 - c = 27

Substituting the values into the quadratic formula, we get: t = (-(-2) ± √((-2)^2 - 4(-4.9)(27))) / (2(-4.9))

Simplifying further, we get: t = (2 ± √(4 + 529.2)) / (-9.8)

Calculating the values inside the square root, we get: t = (2 ± √(533.2)) / (-9.8)

Taking the positive value, we have: t = (2 + √(533.2)) / (-9.8)

Evaluating this expression, we find: t ≈ 1.9 seconds.

Therefore, it takes approximately 1.9 seconds for the stone to fall to the ground.

Final Velocity

To find the final velocity of the stone when it hits the ground, we can use the equation v = u + gt, where: - v is the final velocity, - u is the initial velocity (-2m/s), - g is the acceleration due to gravity (-9.8m/s^2), - t is the time taken for the stone to fall (1.9 seconds).

Substituting the values into the equation, we get: v = -2 + (-9.8)(1.9)

Simplifying, we find: v ≈ -20.02 m/s.

Therefore, the final velocity of the stone when it hits the ground is approximately -20.02 m/s. The negative sign indicates that the velocity is in the opposite direction of the initial velocity.

Summary

In summary, the stone will take approximately 1.9 seconds to fall to the ground from a height of 27m. When it hits the ground, its final velocity will be approximately -20.02 m/s.