Lets say I shot two water rockets into the air...?

Question

The only variable was the payload I placed on the rockets. Both water rockets had the same psi, same water level, etc.
Why does the rocket with a greater payload hit the ground earlier than the one wit ha lighter payload? Doesn't everything fall at the same speed/acceleration?

Answer 1

Red is spot on. Remember that the rocket must be accelerated to get it into the air, and this acceleration is provided by a force:

F = ma

Which means the greater the mass (with the same applied force from the water rocket's thrust mechanism), the lower the acceleration. This means that you can calculate the absolute velocity of each rocket (as a function of time, ignoring all other forces except the thrust and the acceleration downwards due to gravity), and, hence, work out how high each rocket reaches. They will reach different heights and the lighter rocket will go higher. In that way, the heavier rocket will hit the ground again first as they are both accelerated towards the ground at the same speed.

Answer 2

I would guess that the rocket with the greater payload would take more energy to lift to the same height against gravity. Because the energy available is the same, the rocket with the greater payload would not reach the same height and would have less distance to fall.

Answer 3

It would if drag wasn't a factor.