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

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