Answer:
There is no short answer.
Explanation:
Part A
Examining the given situation in the question where an astronaut is trying to get back to the shuttle and trying to figure out a strategy to do so, the best solution in this situation would be to throw an object in the opposite direction of the shuttle since the throwing action will results in the same force being exerted on the astronaut but in the opposite direction and thus pushing him/her towards the shuttle.
Part B
Throwing the object with the biggest mass is the best option in this situation, the force will not be affected by this since the exerted force on the object will be the same, so will the force in the opposite direction but since the lighter the astronauts total weight, the larger the accelaretion will be and therefore throwing the heaviest tool is the best option.
I hope this answer helps.