Astone is thrown with an initial velocity of 20 meters per second straight upward from the edge of a cliff 100 meters above a canyon floor. the stone just misses the cliff'a edge on its way down. (neglect friction)
calculate the time required for the stone to reach its maximum height.
calculate the maximum height of the stone above the edge of the cliff.

I thought you were going to ask how long it takes for the stone to hit
the canyon floor at the bottom of the cliff.  But you're not asking for
anything after the stone barely misses the edge of the cliff on its way
down, and you're only asking about things that happen above the
edge of the cliff. So we don't need to know anything about the cliff,
or its height above anything else.  The thrower might just as well be
standing in his front yard when he throws the stone straight up.

-- Gravity robs 9.8 m/s from the stone's upward speed every second.
So the stone reaches its maximum height, runs out of upward gas, and
starts falling, in  (20 / 9.8) = 2.04 seconds after the toss.

-- Its average speed during that time is (1/2) (20 + 0) = 10 m/s .
In 2.04 seconds at that average speed, it rises (2.04 x 10) = 20.4 meters .