Answer:
1. 0.4 m/s
2. 1.4875 m/s
Explanation:
1.
Following the law of conservation of momentum, the initial sum of momentum equals the final sum of momentum. Usually, momentum, p=mv where m represent mass and v is the velocity.
[tex]m_1v_1+m_2v_2= m_1v_3 +m_2v_4[/tex]
Here subscripts 1 and 2 for mass are for ball and table respectively while for velocity, 1 and 2 are the initial velocities of ball and table respectively, 3 and 4 are final velocities of ball and table respectively.
Substituting mass of ball with 0.2 kg while table with 3 kg, since the table is initially at rest then its initial velocity is zero. Also, the initial velocity of ball we substitute with 14 m/s and final velocity of the ball we substitute with 8 m/s then numerically it will be
[tex](0.2*14)+(3*0)=(0.2*8)+(3v_4)\\v_4=0.4 m/s[/tex]
2.
tex]m_1v_1+m_2v_2= m_1v_3 +m_2v_4[/tex]
Here subscripts 1 and 2 for mass of astronat and space junk respectively while for velocity, 1 and 2 are the initial velocities of astronaut and space junk respectively, 3 and 4 are final velocities of astronaut and space junk respectively.
Substituting mass of astronaut with 80 kg while space junk with 7 kg, since the astronaut is initially at rest then its initial velocity is zero. Also, the initial velocity of space junk we substitute with 11 m/s and final velocity of the space junk we substitute with -6 m/s then numerically it will be
[tex](80*0)+(7*11)=(-6*7)+(80v_4)\\v_4=1.4875m/s[/tex]
