I thought I saw this one earlier and there were people answering. Guess not.
h(t) = 5 + 98t - 4.9t²
h(0) = 5 meters
h(5) = 5 + 98(5) - 4.9(5)² = 372.5 meters
h(10) = 5 + 98(10) - 4.9(10)² = 5 + 980 - 490 = 495 meters
h(15) = 5 + 98(15) - 4.9(15²) = 372.5 meters
h(20) = 5 meters
I'll leave the graphing to you, plot those points
(0,5), (5,372,5),(10,495),(15,372.5) (20,5)
and connect the dots
It's coming down pretty fast at 5 feet up 20 seconds. That last bit is 5/495 or 1% of the trip, so probably double the average speed of around 50m/s so 100msec or .05 sec to go 5 meters.
So it's in the ground at about 20.05 seconds after launch.
Answer: 20.05 meters
