The distance s that an object falls due to gravity varies jointly as the acceleration g due to gravity and the square of the time t of fall. The acceleration due to gravity on the moon is 0.172 that on earth. If a rock falls for 2 seconds on earth, how many seconds would be required for the rock to fall an equal distance on the moon?

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The distance s that an object falls due to gravity varies jointly as the acceleration g due to gravity and the square of the time t of fall.

That means:

s = kgt^2

Where k is a constant of proportionality that you add when removing the proportionality sign.

Let g_m be gravity of moon and g_e be that of Earth.

g_m = 0.172g_e

Since the distance is the same in both cases, you have:

kg_et_e\ ^2 = kg_mt_m\ ^2

Replace gravity of Earth by that of Moon (or vice versa, provided you put the corresponding ratio) then replace the time on Earth.

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