Hi there!
We can use the conservation of momentum to solve.
[tex]m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2'[/tex]
m1 = mass of rocket (40,000 kg)
m2 = mass of gas (300 kg)
v1, v2 = INITIAL velocities of rocket and gas (0 m/s)
v1' = FINAL velocity of rocket (+220 m/s, assuming UP to be positive)
v2' = FINAL velocity of gas (- ? m/s, DOWNWARD so negative)
This is an example of a "recoil" collision, so:
[tex]0 = m_1v_1' + m_2(v_2')[/tex]
Set the two equal:
[tex]m_2(-v_2') = m_1v_1'[/tex]
Plug in the givens:
[tex]300(-v_2') = (40,000)(220)\\\\[/tex]
[tex]\v_2 = \boxed{-29,333.33 m/s}[/tex][tex]v_2 = \boxed{-29,333.33 m/s}[/tex]
