If a ball is thrown vertically upward from the roof of 64 foot building with a velocity of 32 ft/sec, its height after t seconds is s(t)=64+32t–16t2. What is the maximum height the ball reaches "in ft"?

Question

What is the velocity of the ball when it hits the ground (height 0) "in ft/sec"?

Answer 1

as you recall from algebra I, the vertex of a parabola occurs when t = -b/2a. In this case, that is when t = 1

Or, using calculus, since
ds/dt = 32-32t, ds/dt=0 when t=1

s=0 when t=1+√5, so plug that into ds/dt