(a)
The speed at which the astronauts move.
(a)
Answer to Problem 115P
The speed of the firs astronaut is
Explanation of Solution
Given:
The mass of the first astronaut is
The mass of second astronaut is
The mass of the ball is
Calculation:
Let the speed of the ball be
The expression for conservation of linear momentum related to the speed of astronaut and the ball after the first throw is given by,
The expression for the velocity of the ball in the laboratory frame relative to the first astronaut is given by,
Equation (I) can be rewritten as,
The expression for the speed of the ball is given by,
The expression for conservation of momentum for the second astronaut is given by,
Let
The expression for the conservation of momentum is given,
The expression for the speed of the ball in laboratory frame relative to the second astronaut is given by,
Equation (II) can be rewritten as,
Solve further,
The expression for the velocity of the ball in laboratory frame is given by,
The expression for the speed of the astronaut when the catch is taken as,
Conclusion:
Therefore, the speed of the firs astronaut is
(b)
The change in system’s kinetic energy and from where this change came from.
(b)
Answer to Problem 115P
The change in system’s kinetic energy is
Explanation of Solution
Given:
The mass of the first astronaut is
The mass of second astronaut is
The mass of the ball is
Formula Used:
Let
The expression for change in system’s kinetic energy is given by
Calculation:
The change in systems kinetic energy is calculated as,
This energy generally came from the chemical energy in the astronaut’s bodies.
Conclusion:
Therefore, change in system’s kinetic energy is
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Physics for Scientists and Engineers
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