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# Newton's laws of motion: Conservation of momentum

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1) An astronaut loses contact with the hull of a space station and finds himself floating 16m from the station with zero velocity relative to it. Fortunately, he is carrying a 200W flashlight. Turning on the torch he uses it as a "light rocket? If he weighs 150kg, how long will it take to get back to the ship? Is there another way he could use the flashlight to accomplish the same job of returning to the ship?

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1) An astronaut loses contact with the hull of a space station and finds himself floating 16m from the station with zero velocity relative to it. Fortunately, he is carrying a 200W flashlight. Turning on the torch he uses it as a "light rocket". If he weighs 150kg, how long will it take to get back to the ship? Is there another way he could use the flashlight to
accomplish the same job of returning to the ship?

The light can be considered as the beam of Photons. Photons are massless but possesses momentum which is given by
P = E/c
Where E is its energy and c is the speed of light.
The power of flash light is 200 W means it can radiate 200 J light energy per second and hence the rate of change of momentum of the photons is given by

As there is no external force on the system (astronaut and photons), the momentum remains conserved and hence the rate of change of momentum of the astronaut (in opposite direction) will be the same.
As according to Newton's law the force on a body is equal to its rate of change of momentum, the force on the astronaut will be

Thus its acceleration
------------------------------ (1)
And thence the time taken to reach spaceship is given by using second equation of motion as

Or

Yes, he can throw the flashlight in direction opposite to the space station to receive a velocity in the direction of the space station using the same principle of conservation of linear momentum. The time taken in this way will be less.

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