Design a project to determine the specifications $($unstretched length and spring constant k$)$ for the elastic cord to be used at a bungee$-$jumping facility. Participants are to jump from a platform $50$m above the ground. When they rebound, they must avoid an obstacle that extends $4$ m below the point at which they jump.

In determining the specifications for the cord, establish reasonable the safety limits for the minimum distances by which participants must avoid the ground and obstacle. Assume weight of the person as $50$ kg