Answer:
Initial height = 50ft
The flare will be at 58 ft and 1/2 seconds and 1 second
it will hit the ground at 2.67 seconds
Step-by-step explanation:
h(t)= -16t^2 +24t+50
The initial height is 50
We want to find when h = 58
58= -16t^2 +24t+50
Subtract 58 from each side
58-58= -16t^2 +24t+50-58
0 = -16t^2 +24t-8
Factor out -8
0 = -8(2t^2 -3t+1)
Factor inside the parentheses
0 = -8(2t -1) (t-1)
Using the zero product property
2t-1 = 0 t-1 =0
t = 1/2 t=1
The flare will be at 58 ft and 1/2 seconds and 1 second
Both answers make sense, one on the way up and one on the way down.
We need to find when the flare will hit the ground, h=0
0= -16t^2 +24t+50
Using the quadratic formula
-b ±sqrt(b^2-4ac)
--------------------------
2a
-24 ±sqrt(24^2-4(-16)50)
--------------------------
2(-16)
We get solutions for t
t≈-1.1703
t≈2.6703
Time cannot be zero, so it will hit the ground at 2.67 seconds
