A. Find the maximum height it can reach and when it will reach its maximum height.
B.Find when the object hits the ground
C. Write a function that models the height of the object after t seconds
d. Find when the object is above 96 feet.
x= x0 + vot + 1/2 at2
ht = 64 + 48t - 16.1t2 Max occurs at t = - b/2a = -48 / 2(-16.1)
use the value of t determined above in the equation to calculate max height
also use the equation to calculate when above 96ft like this
-16.1t^2 +48t + 64 > 96
-16.1t^2 + 48t -32 >0 use quadratic formula to find t values...there will be two...the time between is when above 96ft
+128475 The function we are working with is
f(t) =-16t^2 + 48t + 64 = answer C
(A ) the max height occurs at -48 / (2 -16) = -48/ -32 = 1.5 seconds
This height is -16(1.5)^2 + 48(1.5) + 64 = 100ft
(B) To find when it hits the ground
-16t^2 + 48t + 64 = 0 divide through by -16
t^2 - 3t - 4 = 0 factor
(t - 4) ( t +1) = 0
The first factor set to 0 gives us a positive time
t - 4 = 0
t = 4 seconds
(D) -16t^2 + 48t + 64 > 96 subtract 96 from both sides
-16t^2 + 48t - 32 > 0 divide trough by -16, chage the dirction of the inequality sign
t^2 - 3t + 2 < 0 factor
(t - 2)( t - 1) < 0
This is true when t is between 1 and 2 seconds
