[Pilot Hopeful]

If g is not constant, well, that is sadistic. However, for a 20-foot difference, we can assume g is nearly constant. Thus, the equations are indeed greatly simplified.

How about starting with energy conservation? Assuming total conservation of mechanical energy, the initial gravitational potential energy of the performer with respect to the surface (mgh) must be equal to his kinetic energy as he lands on the teeter-totter (1/2 mv^2). The only unknown variable is v. Solving for v, we can then determine his momentum, p = mv.

Next, we assume a total energy transfer from performer to baby, i.e.,
E(performer) = E(baby)
(1/2)m(perf)(v(perf)^2) = (1/2)m(baby)(v(baby)^2)

Solving this equation we can determine v(baby). Note that this v(baby) may have x and y components.

Finally, we must solve kinematics equations to find max baby height.