Question

A ball is thrown straight downward from the surface of the moon. Is the maximum height it reaches less than, equal to, or greater than the maximum height reached by a ball thrown upwards on the earth with the same initial speed? Ignore air resistance in both cases

Answer 1

I assume you mean upward

the ball has the same Kinetic energy at release in both cases

(1/2) m V^2 = m g h
so
h = .5 V^2/g

if g is 1/6 that on earth, h will be 6 times higher on the moon