U3.L4.HW: Quadratic Functions: Question 18

Question

Explain your answer.

We are standing on the top of a 1536 feet tall building and launch a small object upward. The object's vertical position, measured in feet, after t seconds is h(t) = -16t² + 160t + 1536. What is the highest point that the object reaches?

________ feet

Answer 1

use algebra:

-16t^2 +160t +1536

complete the square

=-16(t^2 -10t + 25) + 1536 + 25(16)= 1536 +400

=-16(t-5)^2 + 1,936

in vetex form with vertex = (5, 1936) = maximum = 1936 ft in 5 seconds

max height = 1,936 feet

or

use calculus

h=-16t^2 +160t + 1536

h' = -32t +160 = 0

t= 160/32 = 5 seconds

plug 5 into the h equation to get

h(5) = -16(5)^2 + 160(5)+ 1536

= -16(25) + 800+ 1536

= -400 +800+ 1536

= 400+1536

= 1,936 feet maximum height