Question

Find the time th it takes the projectile to reach its maximum height h. express th in terms of v0, ?, and g (the magnitude of the acceleration due to gravity).

Answer 1

The derivative of
  h(t) = (-g/2)t² +v0·t + h0
is
  h'(t) = -gt +v0

This is zero at the maximum height, so the time can be found as
  0 = -gt +v0
  gt = v0
  t = v0/g