A rocket with a lift-off mass of m0 is launched from ground level. During the flight, fuel burns at a constant rate for τ seconds and exhaust gases are ejecting from the bottom of the rocket at β Kg/sec with speed of c m/s relative to the rocket. Ignoring air resistance and assume acceleration due to gravity, g as constant, which of the following expression represents velocity of rocket v(t).
1
\(- c\ln \left[ {\frac{{{m_0} - \beta t}}{{{m_0}}}} \right] - gt\)
2
\(- c\ln \left[ {\frac{{{m_0} - \beta t}}{{{m_0}}}} \right] + gt\)
3
\(- c\ln \left[ {\frac{{{m_0}}}{{{m_0} - \beta t}}} \right] + gt\)
4
\(- c\ln \left[ {\frac{\beta }{{{m_0} - \beta t}}} \right] + gt\)