Question

the exhaust gas of a rocket is expelled at the rate of 1300kg/s, at the velocity of 50000m/s. find the thrust on the rocket in newtron

Answer 1

Answer on Question 59239, Physics, Mechanics, Relativity

Question:

The exhaust gas of a rocket is expelled at the rate of $1300 \, kg/s$, at the velocity of $50000 \, m/s$. Find the thrust on the rocket in newton.

a) $6.5 \cdot 10^{7} N$

b) $3.5 \cdot 10^{7} N$

c) $7.6 \cdot 10^{7} N$

d) $5.7 \cdot 10^{7} N$

Solution:

We can find the thrust on the rocket from the definition of the impulse:

$$F_{t} \Delta t = m \Delta v,$$

here, $F_{t}$ is the force of the thrust on the rocket, $\Delta t$ is the amount of time in which the force is acting, $m$ is the mass of the expelled gas, $\Delta v$ is the rate of change of exhaust gas velocity.

Let's look at our equation. We can see, that in $1 \, s$, $1.3 \cdot 10^{3} \, kg$ of the exhaust gas leaves the rocket at the velocity of $5 \cdot 10^{4} \, m/s$:

$$F_{t} \cdot 1 \, s = 1.3 \cdot 10^{3} \, kg \cdot 5 \cdot 10^{4} \, \frac{m}{s}.$$

Then, we can calculate the force of the thrust on the rocket:

$$F_{t} = \frac{1.3 \cdot 10^{3} \, kg \cdot 5 \cdot 10^{4} \, \frac{m}{s}}{1 \, s} = 6.5 \cdot 10^{7} \, N.$$

Answer:

a) $6.5 \cdot 10^{7} N$

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