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