Answer:
The collision is not elastic. The system increases his kinetic energy m*v₀² times.
Explanation:
Assuming no external forces acting during the collision, total momentum must be conserved.
Considering the information provided, we can write the momentum conservation equation as follows:
m*v₀ = -m*v₀ + 2*m*vf
Solving for vf, we arrive to this somehow surprising result:
vf = v₀ (in the same direction that m was moving before the collision).
In order to determine if the collision was elastic, or not, we need to calculate the kinetic energy of the system before and after the collision:
K₀ = 1/2*m*v₀²
Kf = 1/2*m*v₀² (due to the object of mass m, as the kinetic energy is always positive) + 1/2 (2m) * v₀²
⇒Kf = 1/2*m*v₀² + 1/2 (2m) * v₀² = 3/2*m*v₀²
ΔK = Kf - K₀ = 3/2*m*v₀² - 1/2*m*v₀² = m*v₀²
As there is a net difference between the final and initial kinetic energies, and the total kinetic energy must be conserved in an elastic collision (by definition) we conclude that the collision is not elastic, and the change in the kinetic energy of the system is equal to m*v₀².
The answer is to maintain safety.
To solve the astronaut's problem it is necessary to quickly consider the conservation of the moment.
By definition we know that,
Initial Momentum = Final Momentum
Where,
Human mass
Tank mass
v is the initial and final velocity of each object
In the case of the initial part we know that it is in a state without movement with respect to the ship.
In the case of the final moment there is a speed injection thanks to the oxygen tank, then,
Re-arrange to find the final velocity for astronaut,
Replacing
The astronaut has 4 minutes of air and must travel 200 meters therefore,
Re-arrange to find the time,
<em>He/She will reach the spacecraft within the stipulated time</em>
