Answer:
(a) The thrust of the rocket can be found using the formula:
Thrust = (mass flow rate) x (exhaust velocity)
The mass flow rate is the rate at which mass is expelled from the rocket, which is equal to the burn rate times the mass fraction of fuel:
mass flow rate = burn rate x (mass of rocket) x (mass fraction of fuel)
mass flow rate = 200 kg/s x 20,000 kg x 0.8
mass flow rate = 32,000 kg/s
The exhaust velocity is given as 1.80 km/s. Therefore, the thrust of the rocket is:
Thrust = 32,000 kg/s x 1.80 km/s
Thrust = 57,600 kN
(b) The time it takes to exhaust the fuel can be found using the formula:
time = (mass of fuel) / (burn rate)
The mass of fuel is 80% of the initial mass of the rocket:
mass of fuel = 0.8 x 20,000 kg
mass of fuel = 16,000 kg
Therefore, the time it takes to exhaust the fuel is:
time = 16,000 kg / 200 kg/s
time = 80 seconds
(c) The rocket's speed at the end of its engine burn can be found using the rocket equation:
Δv = (exhaust velocity) x ln[(initial mass) / (final mass)]
The final mass is the mass of the rocket after it has burned all of its fuel, which is:
final mass = (mass of rocket) - (mass of fuel)
final mass = 20,000 kg - 16,000 kg
final mass = 4,000 kg
The initial mass is 20,000 kg. Therefore, the change in velocity is:
Δv = 1.80 km/s x ln[(20,000 kg) / (4,000 kg)]
Δv = 1.80 km/s x ln(5)
Δv = 3.89 km/s
Since the rocket was initially at rest, its final speed is equal to the change in velocity:
final speed = 3.89 km/s
Therefore, the rocket's speed at the end of its engine burn is 3.89 km/s.