An 80-kg astronaut becomes separated from his spaceship. he is 15.0 m away from it and at rest relative to it. in an effort to get back, he throws a 500 gram object with a speed of 8.0 m/s in a direction away from the ship. how long does it take him to get back to the ship?

300 s

Explanation:

The momentum is given by the following equation:

Where is the mass of the object  and is the velocity.

In addition, according to the conservation of linear momentum, we have:

(1)

Where:

is the initial momentum of the astronaut, which is initially at rest

is the final momentum, being , and  

Then (1) is rewritten as:

(2)

Finding te velocity of the astronaut :

(3)

(4)

(5) The negative sign of the velocity indicates it is directed towards the spaceship, however its speed (the magnitude of the velocity vector) is positive

On the other hand we have the following:

(6)

Where the distance between the astronaut and the spacheship and the time. So, we have to find :

(7)

Finally:

the correct choice is a .

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