A rocket in deep space has an exhaust-gas speed of 2000 m/s. When the rocket is fully loaded, the mass of the fuel is five times
1 answer:
Answer:
= 1,386 m / s
Explanation:
The mechanism behind rocket propulsion is defined by the formula
- v₀ =
ln (M₀ / Mf)
Here, v refers to the initial, final, and relative velocities, while M indicates the masses
The provided values include the relative velocity (see = 2000 m / s) and the initial mass, where the mass of the rocket when loaded is represented as (M₀ = 5Mf)
For our analysis, we assume the rocket begins at rest (v₀ = 0)
Once half of the fuel has burnt, the mass ratio indicates that the current mass is
M = 2.5 Mf
- 0 = 2000 ln (5Mf / 2.5 Mf) = 2000 ln 2
= 1,386 m / s
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Please consult the diagram below.
Initially, the system's kinetic energy (KE) is
KE₁ = (1/2)mu²
After the inelastic collision, both masses merge together.
Momentum conservation states that
m*u = 2m*v
Thus,
v = u/2
The final KE is
KE₂ = (1/2)(2m)v²
= m(u/2)²
= (1/4)mu²
= (1/2) KE₁
The reduction in KE is
KE₁ - KE₂ = (1/2) KE₁.
Energy conservation implies that the reduction in KE must be considered as thermal energy.
Result: 1/2
Initially, the system's kinetic energy (KE) is
KE₁ = (1/2)mu²
After the inelastic collision, both masses merge together.
Momentum conservation states that
m*u = 2m*v
Thus,
v = u/2
The final KE is
KE₂ = (1/2)(2m)v²
= m(u/2)²
= (1/4)mu²
= (1/2) KE₁
The reduction in KE is
KE₁ - KE₂ = (1/2) KE₁.
Energy conservation implies that the reduction in KE must be considered as thermal energy.
Result: 1/2
Answer:
The period for the first satellites is 24.46 days, while the second satellites have a period of 37.67 days
Explanation:
Provided:
Distance of the first satellites m
Distance of the second satellites m
Distance of Charon m
Orbit period of Charon days
According to Kepler's third law,
the square of the orbital period correlates to the cube of the semi-major axis.
For the first satellites,
days
For the second satellites,
days
Thus, the orbital period for the first satellites is 24.46 days and for the second satellites, it is 37.67 days