# An astronaut with a mass of #70 kg# is floating in space. If the astronaut throws an object with a mass of #26 kg# at a speed of #1/6 m/s#, how much will his speed change by?

Since we are only interested in the change (or difference) between the two speeds, the actual initial and final speeds of the astronaut are irrelevant. For the sake of argument, we can assume that the astronaut's initial speed is zero. After all, it says "floating in space," so perhaps that really means zero.

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( \Delta v = \frac{{m_{\text{{object}}} \cdot v_{\text{{object}}}}}{{m_{\text{{astronaut}}} + m_{\text{{object}}}}} )

( \Delta v = \frac{{26 , \text{{kg}} \cdot \frac{1}{6} , \text{{m/s}}}}{{70 , \text{{kg}} + 26 , \text{{kg}}}} )

( \Delta v \approx 0.027 , \text{{m/s}} )

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