In order to keep this problem simple, we can assume that the acceleration
of gravity is constant over the distances involved ... 9.8 m/s² .
(When you get super-technical about it, once you go below the surface
of the Earth, gravity actually decreases the deeper you go.)
A useful formula here is:
Distance in free-fall = (1/2) (gravity) (time)²
31 m = (1/2) (9.8 m/s²) (time)²
Divide each side
by 4.9 m/s² : 31 m / 4.9 m/s² = time²
31/4.9 s² = time²
Square root each side: time = √(31/4.9) s
= 2.52 sec (rounded)
