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Motion In A Plane

Question
CBSEENPH11018578

Two projectiles are projected with same velocity at same angle, one on the earth and second on the moon. If the projectile acquires the maximum height of H on the earth, then what will be the maximum height attained by the projectile on the moon?

Solution
Maximum height attained by the projectile on the earth is,
straight H subscript earth equals fraction numerator straight u squared sin squared straight theta over denominator 2 straight g end fraction 
Acceleration due to gravity on the moon is g/6. Therefore maximum height attained by the projectile on the moon is, 
straight H subscript moon equals fraction numerator straight u squared sin squared straight theta over denominator 2 left parenthesis straight g divided by 6 right parenthesis end fraction equals 6 open parentheses fraction numerator straight u squared sin squared straight theta over denominator 2 straight g end fraction close parentheses space equals space 6 straight H subscript earth 
Thus maximum height attained on the moon is six times the maximum height attained on the earth.