Find the maximum height of a model rocket launch algebraically.

Question

A model rocket is launched with an initial velocity of 120 ft/sec from a height of 80ft. The height of the rocket t seconds after it has been launched is given by the function s(t)=-16t^2 +120t + 80. Determine algebraically the time at which the rocket reaches its maximum height and find the maximum height.



Any help is much appreciated.

Answer 1

h(t) =-16t^2 + 120t + 80

take the derivative and set =0

h'(t) =-32t +120 =0

t = 120/32 = 15/4= 3.75 seconds at max height

h(15/4) = -16(15/4)^2 + 120(15/4) + 80 = -225+450+80= 305 feet = max height