Question

An object is launched upward with an initial velocity of 64 feet per second from a platform 80 feet high. Write a model for the object? How many seconds until the maximum height is reached? What will be the maximum height? How many seconds until the object hits the ground

Answer 1

Using one of the equations for costant acceleration 
s = ut + 0.5gt^2 + 80
s = 64t - 16t^2  + 80

s = -16t^2 + 64t + 80
   = -16[ t^2 - 4t) + 80
   = -16 ( t - 2)^2 + 64 + 80
   = -16(t - 2)^2 + 144
Time to maximum height = 2 seconds
Maximum height = 144 ft

Displacement when it hits the ground  = -80 so

-80 = -16t^2 + 64t + 80

solve for t 

t = 5.74 seconds