The physics equation for a perpetual seesaw

I am trying to create a game that envovles two or more people jumping on a seesaw and propelling each other in the air. I need help with the physics equations

Assume no friction no air resistance for now. Ideally when you hit the sweet spot of the seesaw at the very end person B should go a little bit higher than person A who just came down. And if you hit close to the piviot, then the reverse should happen. (I don't know if that is really physics but that is what I am going for)

I know the classic example of two forces on each side and t =r x F so if you had a mass heavier on one side that heavier mass would have to be closer to the piviot

What I am not grasping is if F=ma. And assuming that the masses are all equal then F=a. Now gravity is 9.8/m/s/s on both objects. Is this true even if one of them is at rest on the ground so the seesaw is tilted up?

So because Force is not related to velocity the following doesn't make sense

I would have thought dropping an object from 10 meters would have created more F then from 5 meters if they hit the same spot and have the same mass. So while the velocity increases the acceleration is constant isn't the force constant?

What am I not grasping?

Thank you

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You are using 'g' where it shouldn't be used.

Consider two 1 kg objects that fall and hit the ground, one at 10 m/s, the other at 20 m/s. let's say the impact time for both is 0.1 s, that is to say 0.1 seconds passes after the objects first touches the ground until the objects comes to a complete stop.

a = delta v / time

a1 = (10 m/s) / (0.1 s) = 100 m/s/s

a2 = (20 m/s) / (0.1 s) = 200 m/s/s

F = ma

F1 = (1 kg) * (100 m/s/s) = 100 Newtons

F2 = (1 kg) * (200 m/s/s) = 200 Newtons

The ground exerts twice as much force to decelerate the object that was moving at double the speed.

Regardless, no equations will bring you to what you want, there is no 'sweet spot' that'll make the other person go higher.

What you are talking about is a perpetual motion machine.

http://en.wikipedia.org/wiki/Perpetual_motion

There are many clips on you tube showing circus performers and gymnasts on see saws, watch a few and see where their energy input comes from: climbing ladders to gain gravitational potential energy