Question

Геофизическая ракета, запущенная вертикально с полюса Земли, с момента запуска поднимается с ускорениема = 20 м/c2, разгоняясь до скорости v = 200 м/c. На какую высоту поднимется ракета? С какой скоростью она ударится о Землю? Ускорение свободного падения считать постоянным и равным g = 10 м/c2. Сопротивлением воздуха пренебречь.

Answer 1

1) найдем высоту подъема   h=V^2\2a=200*200\2*20=1000 м



2) при падении h=V^2\2g

Vп=√2gh=√20*1000=141,4 м\с

Answer 2

Calculation of the Height Reached by the Rocket

To calculate the height reached by the rocket, we can use the equations of motion. The rocket starts from rest and accelerates at a rate of 20 m/s^2 until it reaches a velocity of 200 m/s. We can use the following equation to calculate the height:

v^2 = u^2 + 2as

Where: - v is the final velocity (200 m/s) - u is the initial velocity (0 m/s) - a is the acceleration (20 m/s^2) - s is the displacement (height)

Rearranging the equation, we get:

s = (v^2 - u^2) / (2a)

Substituting the given values, we can calculate the height reached by the rocket:

s = (200^2 - 0^2) / (2 * 20) = 2000 meters

Therefore, the rocket will reach a height of 2000 meters.

Calculation of the Impact Velocity with the Earth

To calculate the impact velocity of the rocket with the Earth, we can use the equation of motion for free fall. The rocket will fall from the height it reached with an initial velocity of 0 m/s. The acceleration due to gravity, g, is constant and equal to 10 m/s^2. We can use the following equation to calculate the impact velocity:

v^2 = u^2 + 2as

Where: - v is the final velocity (impact velocity) - u is the initial velocity (0 m/s) - a is the acceleration due to gravity (-10 m/s^2, considering the downward direction) - s is the displacement (height)

Rearranging the equation, we get:

v = sqrt(u^2 + 2as)

Substituting the given values, we can calculate the impact velocity of the rocket:

v = sqrt(0^2 + 2 * (-10) * 2000) = sqrt(40000) = 200 m/s

Therefore, the rocket will impact the Earth with a velocity of 200 m/s.

Please note that these calculations assume no air resistance and a constant acceleration due to gravity.