1. We know that
The carpet is relatively thick, so, it decreases the time of impact. For the increased time of impact, the same force (of gravity) can be achieved by decreasing the impulse "I", which corresponds to a smaller change in momentum and less severe injuries.
2. (a) The mass is
(b) The action of the force on the astronaut by the machine that is rigidly connected to the vehicle's body may reduce the measured acceleration. A method that avoids this is the momentum conservation as it can be done inside the vehicle's space without any rigid connections to its body.
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