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a) Each lifts a 2.0 kg rock. Who has to apply the larger force?

b) Each throws the rock horizontally with initial speed of 6.0 metres per second. Who applies the larger force?

For both questions, I wrote: Fred, because the gravity on Earth is greater than that of the Moon, and so there is a larger force acting upon the rock. But, seeing as it is my answer to BOTH question, I am feeling doubtful, because how can there be the same answer to two questions?