a 4 kg model rocket is launched, shooting 50 kg of burned fuel from its exhaust at an average velocity of 625 m/s. What is the velocity of the rocket after the fuel has burned.? Ignore effects of gravity and air resistance.

To find the velocity of the rocket after the fuel has burned, we can use the principle of conservation of momentum. According to this principle, the total momentum before the fuel is burned is equal to the total momentum after the fuel is burned.

Let's denote the initial velocity of the rocket as V_initial, and the final velocity of the rocket as V_final.

The momentum of an object can be calculated by multiplying its mass with its velocity. So, we have:

Initial momentum = (Mass of rocket + Mass of fuel) * V_initial
Final momentum = Mass of rocket * V_final

According to conservation of momentum:

Initial momentum = Final momentum

(Mass of rocket + Mass of fuel) * V_initial = Mass of rocket * V_final

Now, let's substitute the given values into the equation:

(4 kg + 50 kg) * V_initial = 4 kg * V_final

54 kg * V_initial = 4 kg * V_final

Divide both sides of the equation by 4 kg to isolate V_final:

V_final = (54 kg * V_initial) / 4 kg

Now, we can substitute the given value for V_initial:

V_final = (54 kg * 625 m/s) / 4 kg

V_final = 8406.25 m/s

So, the velocity of the rocket after the fuel has burned is approximately 8406.25 m/s.

To find the velocity of the rocket after the fuel has burned, we can use the principle of conservation of linear momentum. According to this principle, the total momentum before the fuel is burned equals the total momentum after the fuel is burned.

First, let's calculate the initial momentum of the rocket. The rocket has a mass of 4 kg and its initial velocity is zero since it hasn't been launched yet. Therefore, the initial momentum of the rocket is:

Initial momentum of the rocket = Mass × Velocity
= 4 kg × 0 m/s
= 0 kg·m/s

Next, let's calculate the momentum of the burned fuel. The fuel has a mass of 50 kg and is expelled from the rocket with an average velocity of 625 m/s. Therefore, the momentum of the burned fuel is:

Momentum of the burned fuel = Mass × Velocity
= 50 kg × 625 m/s
= 31,250 kg·m/s

Now, since the total momentum before the fuel is burned equals the total momentum after the fuel is burned, we can write the following equation:

Initial momentum of the rocket = Final momentum of the rocket + Momentum of the burned fuel

0 kg·m/s = Final momentum of the rocket + 31,250 kg·m/s

Rearranging the equation, we get:

Final momentum of the rocket = -31,250 kg·m/s

We have a negative sign because the direction of the momentum of the burned fuel is opposite to the direction of the rocket's velocity.

Finally, to find the velocity of the rocket after the fuel has burned, we divide the final momentum of the rocket by its mass:

Velocity of the rocket after the fuel has burned = Final momentum of the rocket / Mass
= -31,250 kg·m/s / 4 kg
= -7,812.5 m/s

So, the velocity of the rocket after the fuel has burned is -7,812.5 m/s. The negative sign indicates that the rocket is moving in the opposite direction of the expelled fuel.

momentum fuel+momentumrocketfinal=0

50*625+4*Vf=0
solve for Vf