a 50 kg astronautejects 100 g of gas from his propulsion pistol at a velocity of 50 m/s. what is his resulting velocity?
m1v1 = m2v2
.1 (50) = 50(vf)
-0.50m/s
m1v1=m2v2
*convert 100g of gas to kg
(.1kg)(50m/s)=(50kg)(V2)
V2={(.1kg)(50m/s)}/50}
V2= -.10 m/s
*the resulting velocity becomes negative because this is an example of a free-fall problem
*objects direction becomes opposite
To find the astronaut's resulting velocity, we can use the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant before and after any event such as the ejection of gas.
The momentum of an object is given by the formula:
Momentum = Mass × Velocity
Before the ejection:
The initial momentum of the astronaut, before ejecting the gas, can be calculated as:
Astronaut's initial momentum = Mass of the astronaut × Initial velocity of the astronaut
After the ejection:
The momentum of the astronaut after ejecting the gas can be calculated as:
Astronaut's final momentum = (Mass of the astronaut + Mass of the gas) × Final velocity
Since no external forces are acting on the astronaut-gas system, the total momentum before and after the ejection remains the same. Therefore, we can set up an equation with the two momentum values equal to each other:
Mass of the astronaut × Initial velocity of the astronaut = (Mass of the astronaut + Mass of the gas) × Final velocity
Plugging in the given values:
(50 kg) × Initial velocity of the astronaut = (50 kg + 0.1 kg) × Final velocity
Simplifying:
50 kg × Initial velocity of the astronaut = 50.1 kg × Final velocity
Now, rearrange the equation to solve for the final velocity:
Final velocity = (50 kg × Initial velocity of the astronaut) / 50.1 kg
Substituting the given values:
Final velocity = (50 kg × 50 m/s) / 50.1 kg
Calculating:
Final velocity ≈ 49.9 m/s
Therefore, the astronaut's resulting velocity after ejecting the gas is approximately 49.9 m/s.