# On Earth, an astronaut and his space suit weigh 1960 N.  While working outside of the international space station weightless in space, the astronaut fires a 100 N rocket backpack for 3 seconds directed away from the station.  What is the resulting velocity of the astronaut and equipment and how far away from the iss is he when the rocket stops firing?

Hello!

As I understand, the rocket backpack provides a constant force of `100 N.` During its work it throws away some mass, therefore the mass of the astronaut with his equipment changes. We don't know how it changes, but I suppose that this change is small (negligible).

The mass `m` of an astronaut with his space suit is his weight on Earth divided by Earth's gravitational acceleration `g=9.8 m/s^2.` His mass is `200 kg.` The mass remains the same in space, while weight may change even on Earth (during a free fall, for example).

By Newton's second law, the astronaut gets a constant acceleration of `a=F/m=100/200=0.5(m/s^2),` where `F` is a force. Therefore his velocity is `V(t)=at` and his displacement is `d(t)=(a t^2)/2` (because the initial speed is zero).

Thus, after `3` seconds the velocity will be `0.5*3=1.5 (m/s)` and the distance will be `(0.5*9)/2=2.25 (m).`

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