Final answer:
The length of the bungee cord at t=7 seconds cannot be determined without additional information. However, the work done to stretch a bungee cord by 16.7 m involves integrating the force function representing the non-linear elastic force, using principles of mechanics and calculus.
Step-by-step explanation:
The problem involves computing work done on a bungee cord, which requires understanding the physics concept of elastic potential energy in mechanics. The given bungee cord exerts a non-linear elastic force represented by F(x) = k1x + k2x3, where k1 = 204 N/m and k2 = -0.233 N/m3. To find out how much work is required to stretch this bungee cord by a distance of 16.7 m, we need to integrate the force function over the stretch of the cord.
The work done, W, is the integral of the force with respect to displacement, so W = ∫ F(x) dx. This calculation involves the application of calculus to determine the area under the curve of the force function, which represents the total work done in stretching the bungee cord.
Although the initial question about the length of the bungee cord at t=7 seconds is not directly answerable with the given information, the question about the maximum length of the bungee during a jump and the work done to stretch the cord are related to the physics of elastic forces. Without specific details regarding the motion or the stretching dynamics of the cord over time, we cannot identify Mark's position at the bungee's maximum length.