Question

Космический корабль начал разгон в межпланетном пространстве, включив ракетный двигатель. Из сопла двигателя ежесекундно выбрасывается 3 кг ( дельта m /дельта t=3 кг/с) горючего газ со скоростью 600 м/с. Определите кинетическую энергию, которую приобретает корабль, пройдя 60 метров после включения двигателя. Изменением массы корабля и полем тяготения пренебречь.(108 кДж). Срочно решите пожалуйста

Answer 1

Ek=F*S
F=dm*V/dt
Ek=dm*V*S/dt=3*600*60=108000 ДЖ=108 кДж

Answer 2

Calculating Kinetic Energy of the Spacecraft

To calculate the kinetic energy acquired by the spacecraft, we can use the formula for kinetic energy:

Kinetic Energy (KE) = 0.5 * mass * velocity^2

Given: - Mass of ejected gas per second, Δm/Δt = 3 kg/s - Velocity of ejected gas, v = 600 m/s - Distance traveled by the spacecraft after the engine is turned on, d = 60 m

First, let's calculate the mass of the gas ejected during the 60 meters of travel.

The mass of the gas ejected during the 60 meters of travel can be calculated using the formula: Δm = Δm/Δt * Δt

Where: - Δm = mass of gas ejected during the 60 meters of travel - Δm/Δt = 3 kg/s (given) - Δt = time taken to travel 60 meters

To find Δt, we can use the formula: v = d/Δt

Where: - v = velocity of the ejected gas (given as 600 m/s) - d = distance traveled by the spacecraft after the engine is turned on (given as 60 m) - Δt = time taken to travel 60 meters

Let's calculate Δt: ``` Δt = d / v = 60 m / 600 m/s = 0.1 s ``` Now, we can calculate the mass of the gas ejected during the 60 meters of travel: ``` Δm = Δm/Δt * Δt = 3 kg/s * 0.1 s = 0.3 kg ```

Next, we can calculate the kinetic energy acquired by the spacecraft using the mass of the gas ejected and the velocity of the gas.

The kinetic energy acquired by the spacecraft can be calculated using the formula: KE = 0.5 * Δm * v^2

Substitute the values: ``` KE = 0.5 * 0.3 kg * (600 m/s)^2 = 0.5 * 0.3 kg * 360000 m^2/s^2 = 54000 J ```

Therefore, the kinetic energy acquired by the spacecraft, after traveling 60 meters following the activation of the engine, is 54,000 J.