This paper explores an optimal control framework for simulating casual human vertical jumps, emphasizing relaxed, low-effort motion. We propose a whole-body motion planning model with realistic contact constraints and a compound objective function that balances achieving sufficient vertical center-of-mass velocity at take-off with minimizing energy expenditure. The framework integrates inverse dynamics and trajectory optimization under physiological constraints. Preliminary comparisons with experimental data show qualitative agreement (CC \(\approx 0.88\) for joint trajectories) in the counter-movement phase and joint kinematics, though quantitative mismatches persist (RMSE \(\approx 20^\circ \) for joint trajectories). Future work will refine objective function weights using inverse optimal control to better align simulations with human data.