Question

Стальной шарик брошен с балкона вертикально вверх. Через время t1 =1с шарик достиг верхней точки траектории. Через время t2 = 3с от начала движения шарик упал на земную поверхность. На какой высоте от земной поверхности находится балкон? Сопротивление воздуха не учитывать. Принять g =10м/с .

Answer 1

Дано:

t1=1с

t2=3с

g=10м/с

------------

h-?

Решение:

\frac{g {t}^{2} }{2} = \frac{10 \times {2}^{2} }{2} = \frac{40}{2} = 20 \: m

ответ:h=20 метров(высота = 20 м)

Answer 2

Calculation of the Height of the Balcony

To calculate the height of the balcony, we can use the equations of motion for an object in free fall. Since the ball is thrown vertically upwards and then falls back down, we can consider two separate motions: the upward motion and the downward motion.

Let's denote the initial velocity of the ball as v0 and the time it takes to reach the highest point of its trajectory as t1. We are given that t1 = 1s.

Using the equation for displacement in the upward motion:

s1 = v0 * t1 - (1/2) * g * t1^2,

where g = 10m/s^2 is the acceleration due to gravity.

Now, let's consider the downward motion. The time it takes for the ball to fall from the highest point to the ground is t2, and we are given that t2 = 3s.

Using the equation for displacement in the downward motion:

s2 = v0 * t2 + (1/2) * g * t2^2.

Since the ball reaches the ground during the downward motion, s2 is equal to the height of the balcony.

To find the height of the balcony, we need to solve the system of equations formed by s1 and s2.

Let's substitute the given values into the equations and solve for s2:

s1 = v0 * t1 - (1/2) * g * t1^2,

s2 = v0 * t2 + (1/2) * g * t2^2.

Substituting t1 = 1s, t2 = 3s, and g = 10m/s^2, we get:

s1 = v0 - (1/2) * g,

s2 = 3v0 + (9/2) * g.

Now, we can solve the system of equations to find v0:

s1 = v0 - (1/2) * g,

s2 = 3v0 + (9/2) * g.

Simplifying the equations, we have:

v0 = s1 + (1/2) * g,

v0 = (s2 - (9/2) * g) / 3.

Setting the two expressions for v0 equal to each other, we can solve for s2:

s1 + (1/2) * g = (s2 - (9/2) * g) / 3.

Simplifying and rearranging the equation, we get:

s2 = 3s1 + (5/2) * g.

Now, let's substitute the given values for s1 and g:

s2 = 3s1 + (5/2) * 10.

Calculating the expression, we find:

s2 = 3s1 + 25.

Therefore, the height of the balcony is 3 times the height reached by the ball in the upward motion, plus 25 meters.

Please note that the exact values of s1 and s2 are not provided in the question, so we cannot calculate the exact height of the balcony without that information.