Question

Камень брошен с поверхности Земли вертикально верх через 4 с падает на землю.Определите высоту подъёма,время падения и скорость камня в момент падения на землю.

Answer 1

Камень кинули вверх при этом Е (кинетическая) = $\frac{m V^{2}}{2}$
Когда камень окажется на высоте его кинетическая энергия = 0 , а потенциальная энергия =$mgh$

$\frac{m V^{2} }{2} =mgh$

$\frac{V ^{2} }{2} =gh$

$\frac{ h^{2} }{2 t^{2} } =gh$

$h=2gt_{1} ^{2}$ , где $t_{1}$ -время подъема

$h = \frac{g t_{2} ^{2} }{2}$  $t_{2}$ - время падения

$2g t _{1} ^{2} = \frac{gt _{2} ^{2} }{y}$

$t ^{2} _{1} = \frac{t ^{2} _{2} }{4}$

$t_{1} = \frac{t _{2} }{2}$

Если $t _{1} =x$, то $t_{2} = 2x$

x+ 2x = 4 c -->    x = 4/3

$t_{2} = \frac{8}{3} =2,7 c$

h = $\frac{10*2,7 ^{2} }{2}$ = 5 m

Answer 2

Calculation of Height, Time, and Velocity of the Falling Stone

To determine the height, time, and velocity of a stone thrown vertically upwards from the surface of the Earth and falling back down after 4 seconds, we can use the equations of motion.

Let's break down the problem step by step:

Step 1: Determine the time taken to reach the maximum height.

When the stone is thrown vertically upwards, it will reach a maximum height before falling back down. The time taken to reach this maximum height can be calculated using the equation:

t = (v - u) / g Where: - t is the time taken, - v is the final velocity (which is 0 when the stone reaches the maximum height), - u is the initial velocity (which is the same as the final velocity when the stone is thrown vertically upwards), - g is the acceleration due to gravity.

Since the stone is thrown vertically upwards, the initial velocity (u) is positive. Therefore, we can rewrite the equation as:

t = u / g Step 2: Calculate the height reached by the stone.

The height reached by the stone can be calculated using the equation:

h = u * t - (1/2) * g * t^2 Where: - h is the height reached, - u is the initial velocity, - t is the time taken, - g is the acceleration due to gravity.

Step 3: Determine the velocity of the stone at the moment it hits the ground.

The velocity of the stone at the moment it hits the ground can be calculated using the equation:

v = u + g * t Where: - v is the final velocity (which is the velocity at the moment the stone hits the ground), - u is the initial velocity, - g is the acceleration due to gravity, - t is the time taken.

Now, let's calculate the values:

Step 1: Calculate the time taken to reach the maximum height.

Since the stone is thrown vertically upwards and falls back down after 4 seconds, the time taken to reach the maximum height is half of the total time:

t = 4 / 2 = 2 seconds

Step 2: Calculate the height reached by the stone.

Using the equation:

h = u * t - (1/2) * g * t^2

We need to know the initial velocity (u) and the acceleration due to gravity (g) to calculate the height. Unfortunately, these values are not provided in the question. Therefore, we cannot determine the exact height reached by the stone.

Step 3: Determine the velocity of the stone at the moment it hits the ground.

Using the equation:

v = u + g * t

Again, we need to know the initial velocity (u) and the acceleration due to gravity (g) to calculate the velocity. Since these values are not provided in the question, we cannot determine the exact velocity of the stone at the moment it hits the ground.

In summary, based on the information provided, we can determine that the time taken to reach the maximum height is 2 seconds. However, we cannot calculate the exact height reached or the velocity of the stone at the moment it hits the ground without knowing the initial velocity and the acceleration due to gravity.

Please let me know if there is anything else I can help you with!