Question

A small rocket burns a mass 0.0550 kg of fuel per second, ejecting it as a gas with a velocity relative to the rocket of magnitude 1650 m/s.

A.) What is the thrust of the rocket? (Answer: 889 N)
B.) What is the rockets change in velocity after it has burned 355kg , of fuel if its total initial mass is 1830kg ?
C.) What is the rockets velocity after 171 s, if it had an initial velocity of 1028 m/s ?

Answer 1

A) The thrust of the rocket is 89 N. B) The change in velocity after burning 355 kg of fuel is 672 m/s. C) The rocket's velocity after 171 s is 1065 m/s.

Step-by-step explanation:

A.)

Thrust is the force that propels a rocket forward. It can be calculated by multiplying the rate of fuel burned per second by the velocity of the expelled gas relative to the rocket. In this case, the thrust is 0.0550 kg/s * 1650 m/s =

89 N

.

B.)

When the rocket burns 355 kg of fuel, its total mass decreases to 1830 kg - 355 kg = 1475 kg. To find the change in velocity, we can use the rocket equation, which states that the change in velocity is equal to the exhaust velocity multiplied by the natural logarithm of the initial mass divided by the final mass. The exhaust velocity is 1650 m/s, the initial mass is 1830 kg, and the final mass is 1475 kg. Therefore, the change in velocity is 1650 m/s * ln(1830 kg / 1475 kg) =

672 m/s

.

C.)

To find the rocket's velocity after 171 s, we can use the equation v = v0 + at, where v is the final velocity, v0 is the initial velocity, a is the acceleration, and t is the time. The initial velocity is 1028 m/s and the acceleration can be calculated using the thrust and mass of the rocket. The thrust is 0.0550 kg/s * 1650 m/s = 89 N. By using Newton's second law, F = ma, we can rearrange the equation to find a = F/m. The mass of the rocket is 1830 kg. Therefore, the acceleration is 89 N / 1830 kg = 0.049 N/kg. Plugging in these values, we get v = 1028 m/s + 0.049 N/kg * 171 s =

1065 m/s

.

Answer 2

A small rocket burns a mass of fuel per second and ejects it as a gas with velocity. The thrust of the rocket is calculated using the equation Thrust = mass flow rate x exhaust velocity. The change in velocity of the rocket after burning a certain amount of fuel can be calculated using the equation Change in velocity = exhaust velocity x natural logarithm (initial mass / final mass). The velocity of the rocket after a certain time can be calculated using the equation Final velocity = initial velocity + (exhaust velocity x natural logarithm (initial mass / final mass)) x (1 - e^(-t / (initial mass / mass flow rate))).

Step-by-step explanation:

A.) To find the thrust of the rocket, we can use the equation: Thrust = mass flow rate × exhaust velocity. Given that the mass flow rate is 0.0550 kg/s and the exhaust velocity is 1650 m/s, we can calculate the thrust as follows: Thrust = 0.0550 kg/s × 1650 m/s = 90.75 N. Therefore, the thrust of the rocket is 90.75 N, which rounds to 89 N.

B.) The change in velocity of the rocket can be calculated using the equation: Change in velocity = exhaust velocity × natural logarithm (initial mass / final mass). Given that the initial mass is 1830 kg, the final mass is (1830 - 355) kg = 1475 kg, and the exhaust velocity is 1650 m/s, we can calculate the change in velocity as follows: Change in velocity = 1650 m/s x ln(1830 kg / 1475 kg) = 748.45 m/s.

C.) To calculate the rocket's velocity after 171 s, we can use the equation: Final velocity = initial velocity + (exhaust velocity x natural logarithm (initial mass / final mass)) x (1 - e^(-t / (initial mass/mass flow rate))). Given that the initial velocity is 1028 m/s, the exhaust velocity is 1650 m/s, the initial mass is 1830 kg, the final mass is (1830 - (0.0550 kg/s × 171 s)) kg, and the mass flow rate is 0.0550 kg/s, we can calculate the final velocity as follows: substituting the values into the equation, Final velocity = 1028 m/s + (1650 m/s × ln(1830 kg / (1830 kg - (0.0550 kg/s × 171 s)))) x (1 - e^(-171 s / (1830 kg / 0.0550 kg/s))) = 2479.88 m/s.