A Bungee jumper of mass m plans to drop starting at rest from a cliff of height H over a river, just coming to rest gently at the river's surface before being pulled back up. The key to a successful experience is to match the Bungee cord's unstretched length L (< H) and force constant k to the jumper's mass m and the jump height H. An additional constraint is that the jumper's upward acceleration during the jump be no greater than some specified maximum value amax. Required:
Derive algebraic expressions for the Bungee cord's appropriate unstretched length L and force constant k in terms of H.