Need help with momentum problem

1. Nov 7, 2004

pkhor

For a safe re-entry into the Earth's atmosphere, the pilots of a space capsule must reduce their speed from 2.6 x 10^4 m/s to 1.1 x 10^4 m/s. The rocket engine produces a backward force on the capsule of 1.8 x 10^5 N. The mass of the capsule is 3800 kg. For how long must they fire their engine? [Hint: Ignore the change in mass of the capsule due to the expulsion of exhaust gases.]

The answer to this problem is 320 seconds, but I have no idea how to get to that answer. I just want to know the formula or theorem that I can use to solve this specific problem. Your help would be highly appreciate.

PS. sorry for my English, I'm not a native speaker.

2. Nov 7, 2004

Pyrrhus

Newton's 2nd Law

$$\sum_{i=1}^{n} \vec{F}_{i} = \frac{d \vec{P}}{dt}$$

Using $\vec{p} = m \vec{v}$

$$\sum_{i=1}^{n} \vec{F}_{i} = \frac{d (m \vec{v})}{dt}$$

The problem states mass is constant therefore it can go out of the derivative.

$$\sum_{i=1}^{n} \vec{F}_{i} = m \frac{d\vec{v}}{dt}$$

For Finitessimals:

$$\sum_{i=1}^{n} \vec{F}_{i} = m \frac{\Delta \vec{v}}{\Delta t}$$

3. Nov 7, 2004

pkhor

My course is Algebra based physics.
I can't understand Calculus, so is there any formula that based on algebra?
Thanks for your respond.

4. Nov 7, 2004

KnowledgeIsPower

Use F=Ma to find the acceleration due to the backward force. You can then find the time needed to reduce their speed to the correct value.

5. Oct 26, 2011

maxwellwest

This problem involves manipulating the impulse-momentum theorem.
We know that Impulse is equal to the change in momentum (I=Δp) where change in momentum is Δp=mv(final)-mv(initial). We also know that Impulse is equal to Force*change in time (I=FΔt). Using these formulas you should be able to solve this question with ease.

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