A certain type of rocket system is proposed for fighting fires. It will be released from an airplane above the fire and use rocket propulsion to hover above the fire for 20 seconds to allow the airplane to clear the area and then explode to disperse the firefighting material. The initial mass can be no more than 500 kg and the firefighting device has a mass of 400kg. The propulsion system structure and other components have a mass of 20% of the propellant mass.
a. What is the minimum exhaust velocity required for this system to work?
b. What is the total impulse for this system?