SOLUTION: h= -16t2 +80t + 50 Use this position polynomial to calculate the following: The height of the object after 2 seconds The height of the object after 5 seconds The maximum h

Question 316746: h= -16t2 +80t + 50
Use this position polynomial to calculate the following:
The height of the object after 2 seconds
The height of the object after 5 seconds
The maximum height of the object
How long the the object will take to reach the ground?
Found 2 solutions by Fombitz, ankor@dixie-net.com:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
1.

.
.
2.

.
.
3.Complete the square to get to vertex form.
The max. height occurs at the vertex.

(5/2,150) is the vertex.

.
.
4.

The time we need is the positive solution,

or approximately
sec.
.
.
.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
h= -16t^2 +80t + 50
;
Use this position polynomial to calculate the following:
:
The height of the object after 2 seconds
h = -16(2^2) + 80(2) + 50
h = -16(4) + 160 + 50
h = -64 + 160 + 50
h = 146 ft
;
The height of the object after 5 seconds
Do the same as above, using t=5
:
The maximum height of the object
Find the axis of symmetry; x = -b/(2a)
in this equation x=t; a=-16: b=80;
t =
t =
t = 2.5 sec; the max height will occur in 2.5 sec
Substitute 2.5 for t to find the max height
h = -16(2.5^2) + 80(2.5) + 50
h = -16(6.25) + 200 + 50
h = -100 + 200 + 50
h = 150 ft is max height
:
How long the the object will take to reach the ground?
when it strikes the ground, h=0, write the equation
-16t^2 + 80t + 50 = 0; solve for t using the quadratic formula
a=-16, b=80, c=50

I'll let you do the math here, the positive solution ~ 5.5 sec
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