A rocket burns fuel at a rate of 281 kg/s and

exhausts the gas at a relative speed of 4 km/s.
Find the thrust of the rocket.
Answer in units of MN.

1 answer

The thrust \( F \) produced by a rocket can be calculated using the formula:

\[ F = \dot{m} v_{e} \]

where:

  • \( F \) is the thrust,
  • \( \dot{m} \) is the mass flow rate of the fuel (in kg/s),
  • \( v_{e} \) is the exhaust velocity (in m/s).

Given:

  • \( \dot{m} = 281 \) kg/s,
  • \( v_{e} = 4 \) km/s \( = 4000 \) m/s (since 1 km = 1000 m).

Now we can substitute the values into the thrust equation:

\[ F = 281 , \text{kg/s} \times 4000 , \text{m/s} \]

Calculating this gives:

\[ F = 1124000 , \text{N} \]

To convert Newtons to MegaNewtons (MN):

\[ F = \frac{1124000 , \text{N}}{10^6} = 1.124 , \text{MN} \]

Thus, the thrust of the rocket is:

\[ \boxed{1.124 , \text{MN}} \]