Motion of a rocket with propellant exhaust gas speed = constant

[arhzz]

Homework Statement

The propellant gas flows out of a rocket with an initial mass of M = 650g at a constant speed of u0 = 200m / s. The consumption of the gas is μ = 200g / s. What is the speed of the rocket relative to Earth t = 1 second after launch?

Relevant Equations

$$ V = u0 * ln \frac M m0 $$

Now this is how I've tried to solve this

$$ v_e = u0 \cdot ln \frac {M} {M- μ \cdot t} $$

After putting in the values I get this;

$$ v_e = 200 * ln 0,36 $$
$$ v_e = 73,54 \frac m s $$

Now I'd say that this is the correct way to do it, but this part is confusing me "What is the speed of the rocket relative to Earth t = 1 second after launch?" This applies to every speed, because every speed is relative to the earth. Is this just an trick too put us off, or something worth considering within the paramets and calculations itself?

Thank you in advance!

 

[PeroK]

"What is the speed of the rocket relative to Earth t = 1 second after launch?" This applies to every speed, because every speed is relative to the earth. Is this just an trick too put us off, or something worth considering within the paramets and calculations itself?

Thank you in advance!

Not all speeds are measured relative to the Earth. It seems quite natural to say "relative to the Earth" here. It's certainly not a trick.

PS If the rocket is only $650g$ then that is a very small rocket. I guess it's supposed to be a firework.

 

[kuruman]

The 200 m/s exhaust velocity of the gas is relative to the rocket. The problem wants to make sure you understand that you shouldn't follow suit and give the final velocity of the rocket relative to itself which is, of course, zero.

 

[haruspex]

$$ v_e = 200 * ln 0,36 $$

.. every speed is relative to the earth.

I think you mean $$ v_e = 200 *\ ln (650/450)=200*0,36 $$

Not every speed is relative to earth. Perhaps you mean that you would have assumed relative to Earth without needing it to be stated?

 

[arhzz]

I think you mean $$ v_e = 200 *\ ln (650/450)=200*0,36 $$

Not every speed is relative to earth. Perhaps you mean that you would have assumed relative to Earth without needing it to be stated?

Yes, I would have assumed relative to Earth without the statement, but all of your answers were of great help, thank you! And yes you are right, it is ln(650/450)

 

[arhzz]

Not all speeds are measured relative to the Earth. It seems quite natural to say "relative to the Earth" here. It's certainly not a trick.

PS If the rocket is only $650g$ then that is a very small rocket. I guess it's supposed to be a firework.

I see, and yes it was very small rocket shown to us in class.

 

[arhzz]

The 200 m/s exhaust velocity of the gas is relative to the rocket. The problem wants to make sure you understand that you shouldn't follow suit and give the final velocity of the rocket relative to itself which is, of course, zero.

I see, thank you!