# Conservation of Momentum Space Ship Problem

• AnhTran
In summary: But it could have been ejected in any direction, including at right angles to the motion of the ship.
AnhTran

## Homework Statement

The payload of a spaceship accounts for 20% of its total mass. The ship is traveling in a straight line at 2100km/hr relative to some inertial observer O. When the time is right, the spaceship ejects the payload, which is moving away from the ship at 500km/hr immediately after the ejection. How fast is the spaceship now moving, as observed by O

## Homework Equations

total momentum before launch equal total momentum after launch
p=mv
v(p)=v(p/s)+v(s) (relative velocity of the payload after launch)
m(s): mass of the body of the ship
v(si): velocity of the body of the ship before launch
v(pi): velocity of the payload before launch
v(sf): velocity of the body of the ship after launch
v(pf): velocity of the body of the ship after launch

## The Attempt at a Solution

since the total mass is not given, I let the mass of the body of the ship equal 1 and the mass of the payload equal 0.25
my equation: m(s)*v(si)+m(p)*v(pi)=m(s)*v(sf)+m(p)*v(pf)
substituting for the variable: 1(2100)+0.25(2100)=1(2100-v(s))+0.25(500+v(s))
v(s) equal -533.33km/hr, which is greater than 500, which shows that the actual velocity of the payload is opposite of velocity of the entire ship before launch. I don't know how I did it wrong so if someone can help me on this I will be very grateful.

The problem does not specify the direction of motion of the payload relative to the direction of the initial motion. Let's assume that the direction is opposite to the velocity of the ship. In the momentum conservation equation all velocities must be relative to the inertial frame. We know what they are initially. If the payload is moving away from the ship backward at 500 km/h as seen from a passenger on the ship and the ship is moving forward at 2100 km/h, what is the velocity of the payload as seen by someone at rest on the inertial frame?

the velocity of the payload as seen by someone at rest at the inertial frame would be 2100km/hr-500km/hr, or 1600km/hr. So if we do not assume the direction, then how do we know which velocity of the payload is the correct one? The velocity of the payload could be 2100+500=2600.

AnhTran said:
So if we do not assume the direction, then how do we know which velocity of the payload is the correct one?
Your guess is as good as mine. Perhaps there is a figure that accompanies the problem. If this has been assigned to you by someone, you can ask them.

AnhTran said:
the velocity of the payload as seen by someone at rest at the inertial frame would be 2100km/hr-500km/hr, or 1600km/hr. So if we do not assume the direction, then how do we know which velocity of the payload is the correct one? The velocity of the payload could be 2100+500=2600.
The payload could have been ejected in any direction, including at right angles to the motion of the ship. But whichever the direction, neither of the two expressions you have written can be correct. The question states:
AnhTran said:
away from the ship at 500km/hr immediately after the ejection
You have taken it to be at 500km/hr relative to the motion of the ship before ejection.

gneill

## 1. What is the conservation of momentum space ship problem?

The conservation of momentum space ship problem is a scenario where a spacecraft is traveling through space and must change its direction or speed in order to reach its destination. This requires the spacecraft to exert a force, which can affect its momentum.

## 2. Why is momentum conservation important in space travel?

Momentum conservation is important in space travel because it helps to ensure that the spacecraft is able to reach its destination with the necessary speed and direction. If momentum is not conserved, the spacecraft may not be able to maneuver properly and could potentially miss its target.

## 3. How does a spacecraft conserve momentum while changing its direction?

A spacecraft can conserve momentum while changing its direction by using thrusters or other propulsion systems to exert a force in the opposite direction of the desired change. This counteracting force helps to maintain the overall momentum of the spacecraft.

## 4. Can momentum be conserved while changing the speed of a spacecraft?

Yes, momentum can also be conserved while changing the speed of a spacecraft. This can be achieved by using a combination of thrust and mass distribution, such as releasing or absorbing fuel, to maintain the overall momentum of the spacecraft.

## 5. Are there any limitations to the conservation of momentum in space travel?

While the conservation of momentum is a fundamental principle in physics, there are some limitations to its application in space travel. For example, external forces such as gravitational pull or collisions with other objects can affect the momentum of a spacecraft and may need to be taken into consideration during maneuvers.

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