Math Solutions

Solution: The upward velocity of a rocket can be computed by the following formula: v=u ln ((m_0)/(m_0)-q t)-g t where v= upward velocity, u= velocity

Question: The upward velocity of a rocket can be computed by the following formula:

\[v=u \ln \left(\frac{m_{0}}{m_{0}-q t}\right)-g t\]

where \(v=\) upward velocity, \(u=\) velocity at which fuel is expelled relative to the rocket, \(m_{0}=\) initial mass of the rocket at time \(t=0, q=\) fuel consumption rate, and \(g=\) downward acceleration of gravity (assumed constant \(\left.=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\). If \(u=\) \(1800 \mathrm{~m} / \mathrm{s}, m_{0}=160,000 \mathrm{~kg}\), and \(q=2500 \mathrm{~kg} / \mathrm{s}\), determine how high the rocket will fly in \(30 \mathrm{~s}\).

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