A 68.5 kgkg astronaut is doing a repair in space on the orbiting space station. She throws a 2.25 kgkg tool away from her at 3.50 m/sm/s relative to the space station.Part AWith what speed will she begin to move?Express your answer with the appropriate units.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeΔvΔ𝑣 =nothingnothingSubmitRequest AnswerPart BIn what direction will she begin to move?She moves opposite to the direction in which she throws the tool.She moves in the direction in which she throws the tool.
Question
A 68.5 kgkg astronaut is doing a repair in space on the orbiting space station. She throws a 2.25 kgkg tool away from her at 3.50 m/sm/s relative to the space station.Part AWith what speed will she begin to move?Express your answer with the appropriate units.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeΔvΔ𝑣 =nothingnothingSubmitRequest AnswerPart BIn what direction will she begin to move?She moves opposite to the direction in which she throws the tool.She moves in the direction in which she throws the tool.
Solution
Part A
The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. In this case, the astronaut and the tool form an isolated system. Before the astronaut throws the tool, the total momentum of the system is zero because they are both stationary. After the tool is thrown, the total momentum must still be zero.
The momentum of the astronaut is her mass times her velocity (m_a * v_a), and the momentum of the tool is its mass times its velocity (m_t * v_t). Setting the total momentum before the throw (0) equal to the total momentum after the throw (m_a * v_a + m_t * v_t) gives us:
0 = m_a * v_a + m_t * v_t
We can rearrange this equation to solve for the astronaut's velocity (v_a):
v_a = - (m_t * v_t) / m_a
Substituting the given values:
v_a = - (2.25 kg * 3.50 m/s) / 68.5 kg = -0.115 m/s
The negative sign indicates that the astronaut's velocity is in the opposite direction of the tool's velocity.
Part B
As indicated by the negative velocity, the astronaut will begin to move in the opposite direction to which she throws the tool.
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