Energy conservation in bungee jumping

Steps:

• Gravitational PE is zero at lowest point, so at distance fallen x (0 to h), it equals mg(h - x), decreasing linearly from mgh to 0.
• Elastic PE is zero until rope stretches; then (1/2)k(y)^2 where y = x - L (L = unstretched length), increasing quadratically with extension.
• Total mechanical energy conserved: initial gravitational PE converts to elastic PE at lowest point.
• Graph vs. x shows linear gravitational decrease and quadratic elastic rise, meeting at x = h.

Why A is correct:

• Matches definitions: gravitational PE linear in height (PE = mgh), elastic PE quadratic per Hooke's law (PE = ½kx²).

Why the others are wrong:

• B: Elastic PE shown linear, violating Hooke's law quadratic dependence.
• C: Gravitational PE curved, ignoring linear relation to height.
• D: Energies don't sum to constant total, breaking conservation.

Final answer: A