Answer :
The velocity of the rocket of mass 40 kg after all the fuel is gone is 44.8 m/s.
What is velocity?
Velocity is the ratio of displacement to time.
To calculate the velocity of the rocket after all the fuel is gone, we use the formula below.
Formula:
- v = mV/M................. Equation 1
Where:
- v = Velocity of the rocket after all the fuel is gone
- M = Mass of the rocket
- V = Velocity of the fuel
- m = Mass of the fuel
From the question,
Given:
- m = 16 kg
- M = 40 kg
- V = 112 m/s
Substitute these values into equation 2
- v = (16×112)/40
- v = 44.8 m/s
Hence, the velocity of the rocket is 44.8 m/s.
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Final answer:
Using the principle of conservation of momentum, the velocity of the rocket after all the fuel is gone is calculated to be 74.67 m/s.
Explanation:
In this problem, we can use the principle of conservation of momentum to find the velocity of the rocket after it has launched all its fuel. The initial total momentum of the system (rocket plus fuel) is zero, as the system is at rest. After the rocket has launched its fuel, the momentum must still sum to zero because there are no external forces.
Momentum before = Momentum after
0 = -m_fuel.v_fuel + m_rocket.v_rocket
Here m_fuel is the mass of the fuel (16 kg) and v_fuel is the fuel velocity relative to the rocket (112 m/s) and m_rocket is the mass of the rocket without fuel (40 kg - 16 kg = 24 kg) and v_rocket is the rocket velocity (to be found).
We can rearrange this to find v_rocket:
v_rocket = (m_fuel.v_fuel) / m_rocket = (16 kg * 112 m/s) / 24 kg = 74.67 m/s
So the rocket velocity after all the fuel is gone would be 74.67 m/s.
Learn more about Physics of Rocket Propulsion here:
https://brainly.com/question/15363207
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