Question

С поверхности Земли вертикально вверх пущена ракета со скоростью v=5 км/с. На какую высоту она поднимется?

Answer 1

Дано: v=5км/c

Найти: h

                                Решение:

Ек=(m*v^2)/2

Конечная кинетическая скорость равна 0 

Разность потенциальных энергий между положением ракеты на поверхности Земли = Еp

Ep=m*g*h

Из закона сохранения энергии следует, что Ek=Ep

(m*v^2)/2=m*g*h

h=v^2/2g=(5000м/с^2)/2*9,81м/с^2=1,27*10^6м=1270км

Ответ:1270 км.

Answer 2

Calculating the Maximum Height of a Rocket Launched Vertically

To calculate the maximum height reached by a rocket launched vertically from the Earth's surface with a velocity of v=5 km/s, we can use the equations of motion and the principles of kinematics.

Using the Equations of Motion

The maximum height reached by the rocket can be calculated using the following equation: v^2 = u^2 + 2as Where: - v = final velocity (which is 0 at the maximum height) - u = initial velocity (given as 5 km/s) - a = acceleration due to gravity (-9.81 m/s^2, assuming downward direction as negative) - s = displacement (the maximum height we want to find)

Calculation

Using the given velocity of v=5 km/s and the acceleration due to gravity of -9.81 m/s^2, we can calculate the maximum height reached by the rocket.

First, we need to convert the velocity from km/s to m/s: 5 km/s = 5000 m/s

Now, we can use the equation to find the maximum height: 0 = (5000 m/s)^2 + 2*(-9.81 m/s^2)*s

Solving for s: s = (5000 m/s)^2 / (2*9.81 m/s^2)

Maximum Height Calculation

Using the above equation, the maximum height can be calculated as follows: s ≈ 1275512.5 meters

Therefore, the rocket will reach a maximum height of approximately 1275512.5 meters when launched vertically from the Earth's surface with a velocity of v=5 km/s.