A rocket expels propellant at \(18\,\mathrm{kg\,s^{-1}}\) with exhaust speed \(2200\,\mathrm{m\,s^{-1}}\). Find the thrust.

A rocket has \(v_e=2500\,\mathrm{m\,s^{-1}}\) and mass ratio \(m_0/m_f=3.0\). Find the ideal \(\Delta v\).

A deep-space rocket needs \(\Delta v=1800\,\mathrm{m\,s^{-1}}\) with \(v_e=3000\,\mathrm{m\,s^{-1}}\). Find the required mass ratio.

A vertical rocket has mass \(1200\,\mathrm{kg}\), thrust \(18000\,\mathrm{N}\), and negligible drag. Find its initial upward acceleration near Earth.

A rocket burns from \(900\,\mathrm{kg}\) to \(600\,\mathrm{kg}\) at mass flow rate \(15\,\mathrm{kg\,s^{-1}}\). Find the burn time.

A deep-space rocket has dry final mass \(800\,\mathrm{kg}\), exhaust speed \(2500\,\mathrm{m\,s^{-1}}\), and required \(\Delta v=1500\,\mathrm{m\,s^{-1}}\). Find the initial mass and propellant mass.

A vertical rocket burns from \(1200\,\mathrm{kg}\) to \(800\,\mathrm{kg}\) in \(20\,\mathrm{s}\) with \(v_e=2500\,\mathrm{m\,s^{-1}}\). Ignoring drag, find the burnout speed from rest including gravity loss.

A rocket stage has \(v_e=3200\,\mathrm{m\,s^{-1}}\). Derive and calculate the propellant mass fraction needed for \(\Delta v=2400\,\mathrm{m\,s^{-1}}\), ignoring external forces.

A vertical rocket starts from rest with \(m_0=900\,\mathrm{kg}\), burns to \(m_f=600\,\mathrm{kg}\) at \(15\,\mathrm{kg\,s^{-1}}\), and has \(v_e=2200\,\mathrm{m\,s^{-1}}\). Ignoring drag, find the burnout speed and check whether it initially lifts off. State assumptions.

For a vertical rocket with constant exhaust speed \(v_e\), constant mass flow rate \(\alpha\), initial mass \(m_0\), final mass \(m_f\), and uniform gravity \(g\), derive the burnout speed from rest and the condition for positive upward acceleration throughout the burn. State assumptions and interpret the condition.