A spring-loaded gun is cocked by compressing a short, strong spring by a distance d. The gun fires a signal flare of mass m directly upward. The flare has speed v₀ as it leaves the spring and is observed to rise to a maximum height h above the point where it leaves the spring. After it leaves the spring, effects of drag force by the air on the packet are significant. (Express answers in terms of m, v₀, d, h, and g , the acceleration due to gravity.) 

(a) How much work is done on the spring in the course of the compression? 

(b) What is the value of the spring constant k? 

(c) How much mechanical energy is converted to thermal energy because of the drag force of the air on the flare between the time of firing and the time at which maximum elevation is reached?