An astronaut with a mass of $85 kg$ is floating in space. If the astronaut throws an object with a mass of $5 kg$ at a speed of $1/4 m/s$ , how much will his speed change by?

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Answer 1 · 2016-05-16T08:34:13

$v_a^'=-0.015" " m/s$

$m_a=85 " "kg " mass of astronaut"$

$v_a=0" velocity of astronaut before event"$

$P_a=m_a*v_a=85*0=0" momentum of astronaut before event"$

$m_o=5" "kg$

$v_o=0" velocity of object before event"$

$P_o=m_o*v_o=5*0=0" momentum of object before event"$

$P_i=P_a+P_o" "P_i=0 " total momentum before event"$

$v_a^'="velocity of astronaut after event"$

$P_a^'=m_a*v_a^'=85*v_a^'" momentum of astronaut after event"$

$P_o^'=m_o*v_o^'=5*1/4=5/4 kg*m/s" object's momentum after event"$

$P_f=P_a^'+P_o^'$

$P_f=85*v_a^'+5/4" total momentum after event"$

$P_i=P_a$

$0=85*v_a^'+5/4$

$85*v_a^'=-5/4$

$v_a^'=-5/(85*4)$

$v_a^'=-0.015" " m/s$

An astronaut with a mass of 85 kg85 kg is floating in space. If the astronaut throws an object with a mass of 5 kg5 kg at a speed of 1/4 m/s1/4 m/s, how much will his speed change by?