An object is thrown upward at a speed of 115 feet per second by a machine from a height of 20 feet off the ground. The height h of the object after t seconds can be found using the equation

Question

An object is thrown upward at a speed of 115 feet per second by a machine from a height of 20 feet off the ground. The height  of the object after  seconds can be found using the equation 

When will the height be 102 feet? _____

When will the object reach the ground? _____

Answer 1

h(t)=-16t^2+115t+20

102=-16t^2+115t+20

-16t^2+115t-82=0

use the quadratic formula

t=-115/-32 + or - (-1/32)sqr(115^2-4(-16)(-82))

that's when it reaches 102 feet,

set h=0 to find when it hits the ground

0=-16t^2+115t+20

use the quadratic formula & solve for t

in each case you will get 2 answers, one may be negative and ignored