A sounding rocket is to be launched vertically from the earth's surface. It is to be designed for a 350-kg payload that must not suffer an acceleration greater than 5 g during the burning period. The maximum propellant mass is 1000 kg, and the structural efficiency factor e is 0.1. The solid propellant rocket motor that will be designed for this vehicle is expected to have a specific impulse of 250 s. Taking g = ge and neglecting aerodynamic drag, determine: 

a. The minimum allowable burning period, 

b. The maximum height attainable, 

c. The height allowable if the maximum payload acceleration were limited to 4 g.