Carbon-14 is a naturally-occuring, stable isotope that is commonly used is scientific studies as a tracer and to date artifacts.
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(a) At its maximum height, the ball's vertical velocity is 0. Recall that
Then at the maximum height , we have
(b) The time the ball spends in the air is twice the time it takes for the ball to reach its maximum height. The ball's vertical velocity is
and at its maximum height, so that
which would mean the ball spends a total of about 5.6 seconds in the air.
(c) The ball's horizontal position in the air is given by
so that after 5.6 seconds, it will have traversed a displacement of