An astronaut with a mass of #75 kg# is floating in space. If the astronaut throws an object with a mass of #8 kg# at a speed of #1/8 m/s#, how much will his speed change by?

Question

An astronaut with a mass of #75 kg# is floating in space.  If the astronaut throws an object with a mass of #8 kg# at a speed of #1/8 m/s#, how much will his speed change by?

Charlotte Aaron · Accepted Answer

#v_a=-0,01bar3" m/s"# #m_a:"mass of astronaut"# #v_a:" velocity of astronaut after event"# #v_o:"velocity of object"# #m_o:"mass of object"# #0=m_a*v_a+m_o*v_o" momentum equation"# #0=75*v_a+cancel(8)*1/cancel(8)# #0=75*v_a+1# #-1=75*v_a# #v_a=-1/75# #v_a=-0,01bar3" m/s"#

William Audy · Answer

undefined The astronaut's speed change can be calculated using the law of conservation of momentum:

$$ \text{Initial momentum} = \text{Final momentum} $$

$$ (m_{\text{astronaut}} \times v_{\text{initial, astronaut}}) + (m_{\text{object}} \times v_{\text{initial, object}}) = (m_{\text{astronaut}} \times v_{\text{final, astronaut}}) + (m_{\text{object}} \times v_{\text{final, object}}) $$

$$ (75 \, \text{kg} \times 0) + (8 \, \text{kg} \times 1/8 \, \text{m/s}) = (75 \, \text{kg} \times v_{\text{final, astronaut}}) + (8 \, \text{kg} \times v_{\text{final, object}}) $$

$$ v_{\text{final, astronaut}} = \frac{(8 \, \text{kg} \times 1/8 \, \text{m/s})}{75 \, \text{kg}} $$

$$ v_{\text{final, astronaut}} = \frac{1}{75} \, \text{m/s} $$