Question

What is the acceleration of a 5000-kg rocket taking off from the Moon, where the acceleration due to gravity is 1.6 m/s², if the rocket expels 8.00 kg of gas per second at an exhaust velocity of 2.20 x 10³ m/s?

Answer 1

The acceleration of the rocket is $1.92 m/s^2$

Explanation:

The impulse exerted by the gas expelled by the rocket is equal to the change in momentum of the gas. Mathematically:

$F\Delta t = \Delta m v$

which can be rewritten as

$F=\frac{\Delta m}{\Delta t}v$

F is the force exerted on the rocket

$\frac{\Delta m}{\Delta t}=8.0 kg/s$ is the amount of mass of gas expelled per second

$v=2.20\cdot 10^3 m/s$ is the velocity of the gas

Solving for F,

$F=(8.0)(2.20\cdot 10^3)=17,600 N$

This force acts upward, but we also know that there is another force acting on the rocket, the force of gravity, acting downward. Its magnitude is

$W=mg=(5000 kg)(1.6 m/s^2)=8000 N$

where

m = 5000 kg is the mass of the rocket

$g=1.6 m/s^2$ is the acceleration of gravity

Therefore, the net force on the rocket is:

$F_{net}=F-W=17,600 - 8000 = 9600 N$

Now we can find the acceleration of the rocket by applying Newton's second law; we find:

$F_{net}=ma\\a=\frac{F_{net}}{m}=\frac{9600}{5000}=1.92 m/s^2$

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