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A 40,000kg rocket traveling at 220 m/s expels 300kg worth of gases at what velocity?

Sagot :

Leenaidn

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]

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