What is the minimum speed that a thrown ball would need to just reach the ceiling?

Question

The ceiling of an arena is 38 m above the floor. What is the minimum speed that a thrown ball would need to just reach the ceiling?

Answer 1

27.3 meters per second would get the ball to just reach the ceiling before falling back down

-4.9t^2 + Vo(t) = 38 and

the derivative

-9.8t + Vo = 0 are two equations whose solution is t = 2.785 seconds at maximum height

and Vo = 27.3 meters per second as the initial velocity

the derivative gives the time and velocity for maximum height