An astronaut with a mass of $75 k g$ $75 kg$ is floating in space. If the astronaut throws a $7 k g$ $7 kg$ object at a speed of $\frac{5}{4} \frac{m}{s}$ $5/4 m/s$ , how much will his speed change by?

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Answer 1 · 2016-05-13T19:43:50

$vec v_a^'=-0.12" " m/s$

$"momentum before event:"$
$.............................................$

$vec P_a=m_a*vec v_a" momentum of astronaut"$
$vec P_a=75*0=0$

$vec P_o=m_o*vec v_o" momentum of object "$
$vec P_o=7*0=0$

$Sigma P_b=0+0=0" total momentum"$

$"momentum after event:"$
$...........................................$

$P_a^'=m_a*v_a^'$
$vec P_a^'=75*vec v_a^'$

$vec P_o^'=m_o*vec v_o^'$
$vec P_o^'=7*5/4=35/4" " kg*m/s$

$Sigma vec P_a=P_a^'+P_o^'$
$Sigma vec P_a=75*vec v_a^'+35/4$

$"in this event momentum is conserved"$
$...............................................................$

$Sigma vec P_b=Sigma vec P_a$
$0=75*vec v_a^'+35/4$

$75*vec v_a^'=-35/4$

$vec v_a^'=-35/300$

$vec v_a^'=-0.12" " m/s$

An astronaut with a mass of 75 kg75kg75 kg is floating in space. If the astronaut throws a 7 kg7kg7 kg object at a speed of 5/4 m/s54ms5/4 m/s, how much will his speed change by?