my math problem

Question

. A toy rocket is launched by a boy from a building which is 60 feet high. The formula given for the maximum height that this toy rocket could reach is defined by. Find the maximum height that this rocket reached. How long would it take to reach that height in seconds?

Answer 1

h(t) = -16t^2 + vot + 60

max height is when velocity = 0

h'(t) = v(t) = -32t + vo

max height is at time t = vo/32

max height is

h(vo/32) = -16(vo/32)^2 + vo(vo/32) + 60

= -vo^2/64 + vo^2/32 +60

= vo^2/64 + 60 feet

just plug in the value of the initial velociy = vo