A spacecraft needs to be slowed down from a speed of 96m/s to 8.2m/s. This can be done by firing an object as the spacecraft is moving. If the mass of the spacecraft is 6730kg and the object is 50kg, calculate the velocity of the ejected object.
As we have there is object being fired out of the front of the spaceship we know the ship will have a lower velocity than before using the conversation of momentum. "The total momentum of a system is the same before and after providing no external forces are present" and that momentum is the product of the velocity and mass of an object. Therefore, we simply calculate the momentum before ejection. i.e. total mass (mass of ship plus object, 6730kg+50kg=6780kg) multiped by originally velocity, 96m/s. Giving the momentum at the start of 650880kgm/s. next we consider the total momentum after, which the new momentum of the ship (smaller now as it slowed down) plus the momentum of the object. New momentum if the ship is the new velocity (8.2m/s) multiped by its mass (6730kg). 55186kgm/s. and the object will be its mass (50kg) multiped by x m/s. 50x kgm/s. the sum if these two values will the starting momentum.
650880 = 55186 + 50x
50x = 595694
X = 11913.88m/s
This means the ejected object will need velocity of 11913.88 m/s.
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