Question

A small rocket with 15 kN thrust burns 250 kg of fuel in 30 s. What is the exhaust speed of the hot gases?

Short answer

The exhaust speed is$1800m/s$

Step-by-step solution

Step 1. Given information

Thrust, $F=15kN$

Mass, $m=250kg$

Time, $t=30s$

To evaluate the exhaust speed.

Step 2. Analyze and evaluate

The exhaust gas and rocket system maintain their momentum. The force equal to the product of the exhaust speed and the rate at which fuel is burnt is known as thrust.

$$\begin{gathered} F_{\text{thrust}}=v_{ex}R=v_{ex}\left(\frac{dm}{dt}\right) \\ {v}_{ex}=\frac{F_{\text{thrust}}}{(dm/dt)} \end{gathered}$$

Now, the rate is, $\frac{dm}{dt}=\frac{250kg}{30s}=8.33kg/s$$\frac{dm}{dt}=\frac{250kg}{30s}=8.33kg/s$

Substitute and evaluate,

$v_{ex}=\frac{15000}{8.33}=1800m/s$