The acceleration due to gravity on the moon is about one-sixth its value on earth. If a baseball reaches a height of 66 m when thrown upward by someone on the earth, what height would it reach when thrown in the same way on the surface of the moon?

I found: ##396m##

We can use the relationship from kinemamatics: ##color(red)(v_f^2=v_i^2+2ad## with: ##v_f=## final velocity which is zero at the top; ##v_i=## initial velocity (the same on Earth and on the Moon I suppose); ##a=## accelration of gravity (##=g## downwards); ##d=## distance (height in this case).

We have:

On Earth: ##0=v_i^2-2g*66## so that ##v_i^2=2g*66##

On the Moon: ##0=v_i^2-2/6gd## so that: ##v_i^2=2/6gd##

so considering the same values for ##v_i^2## we can write: ##2cancel(g)*66=2/6cancelgd## ##d=6*66=396m##