Answer:
The force of gravity, g = 9.8 m/s2
Gravity accelerates you at 9.8 meters per second per second. After one second, you're falling 9.8 m/s. After two seconds, you're falling 19.6 m/s, and so on.
Time to splat: sqrt ( 2 * height / 9.8 )
It's the square root because you fall faster the longer you fall.
The more interesting question is why it's times two: If you accelerate for 1 second, your average speed over that time is increased by only 9.8 / 2 m/s.
Velocity at splat time: sqrt( 2 * g * height )
This is why falling from a higher height hurts more.
Energy at splat time: 1/2 * mass * velocity2 = mass * g * height
Explanation:
