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An astronaut with a mass of #95 kg# is floating in space. If the astronaut throws an object with a mass of #9 kg# at a speed of #7/4 m/s#, how much will his speed change by?

Answer 1

0.17 m/s

Using conservation of momentum we know #p_i = p_f# where i means initial and f, final. If we use the subscript a for the astronaut and o for the object we get:

#m_a . Deltav_a = m_o . Deltav_o#

This means that we can rearrange for #v_a# as the subject.

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Answer 2

Nora Arzate

To find the change in the astronaut's speed, you can use the principle of conservation of momentum. The total momentum before the throw is equal to the total momentum after the throw. Therefore, you can use the equation ( m_{astronaut} \times v_{astronaut, initial} = (m_{astronaut} + m_{object}) \times v_{final} ) to solve for the final velocity of the astronaut. Then, subtract the initial velocity of the astronaut from the final velocity to find the change in speed. After substituting the given values, the change in speed is approximately ( -\frac{5}{38} ) m/s.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.