Question

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.

Answer 1

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:

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