Assignment:
"The launching mechanism of a toy gun consists of a spring of unknown spring constant. If the spring is compressed a distance of 0.139 m and the gun fired vertically, the gun can launch a 25.1g projectile from rest to a maximum height of 24.5 m above the starting point of the projectile. Neglecting all resistive forces, determine the spring constant."
Provide complete and step by step solution for the question, use formulas.