A deranged person (we'll call him Fred, 'kay?) steps off a 10-story building that's roughly 100 feet (about 30.48 meters) tall. The rate of acceleration due to gravity is 9.81 meters per square second. How long is the free-fall, and what is the final velocity right before impact?
Distance = 30.48 meters
Acceleration = 9.81 meters per square second
Time = ?
Final Velocity = ?
Alright. Time can be determined by finding the square root of twice the distance divided by acceleration. In other words:
Time = squareroot(2*distance/acceleration)
If we plug our known variables into the equation, we find that the length of the free fall is about 2.49 seconds.
Two and a half seconds.
To get a proper feel for how eerily short that amount of time is, count the seconds out loud.
One one-thousand, two one-thousand, three one- SPLAT.
Two and a half seconds before Fred's organs rupture instantly on impact. How utterly disturbing.
But wait, we haven't determined the final velocity yet! Maybe our buddy survived the fall after all...
Final velocity is determined by multiplying the rate of acceleration by time.
Final velocity = acceleration*time
If we plug our current variables into this equation, we discover that Freddy hit concrete at about 24.4 meters per second. Hmm. That doesn't sound too bad. Maybe we'll pick him up a gift on our way over to the hospital...
Oh, wait, I forgot. We Americans are little rebels, aren't we? Those numbers don't mean a thing in real life, because we don't use the metric system. How silly of me. Let me just convert that answer real quick...
Final velocity = 87.9 mph
Ohh... Well then. Come to think of it, this is a wonderful time of year to wear black...