A model rocket is launched from a raised platform at a speed of 112 feet per second. Its height in feet is given by h(t) = -16t 2 + 112t + 20 (t = seconds after launch). After how many seconds does the object reach its maximum height?

1 Answer
Mar 25, 2018

#=> t = 3.5# seconds

Explanation:

We are given a function that describes the position of the rocket:

#=>h(t) = -16t^2+112t+20#

We can differentiate this function to obtain a function for the velocity of the rocket:

#=>v(t) = h'(t) = -32t+112#

When the rocket reaches a speed of #0#, it will be at its max height. So we set #v(t)# equal to #0#:

#=>-32t+112 = 0#

#=>-32t = -112#

#=> t = 3.5# seconds