A space satellite has a total mass of 500kg. A portion of mass 20kg is ejected a velocity of 10ms-1 . Calculate the recoil velocity of the remaining portion (ignoring the initial velocity of the satellite).
To calculate the recoil velocity of the remaining portion of the satellite, we can use the principle of conservation of momentum. According to this principle, the total momentum before the ejection is equal to the total momentum after the ejection.
The momentum of an object is given by the product of its mass and velocity. So, initially, the momentum of the satellite (before ejection) can be expressed as:
Momentum_before = Mass_satellite * Velocity_satellite
After the portion is ejected, the momentum of the remaining portion can be expressed as:
Momentum_after = Mass_remaining * Velocity_remaining
Since the total momentum before and after the ejection must be equal, we can write the equation:
Momentum_before = Momentum_after
Mass_satellite * Velocity_satellite = Mass_remaining * Velocity_remaining
Now we can substitute the given values into the equation:
500 kg * 0 m/s = (500 kg - 20 kg) * Velocity_remaining
Simplifying the equation:
0 = 480 kg * Velocity_remaining
To solve for Velocity_remaining, divide both sides of the equation by 480 kg:
Velocity_remaining = 0 / 480 kg
Therefore, the recoil velocity of the remaining portion of the satellite is 0 m/s.
Please note that this result assumes the satellite was at rest initially. If it had an initial velocity, the calculation would include its momentum as well.