SOLUTION: A missile is fired vertically into the air. The distance s (in feet) above the ground as a function of time t (in seconds) is given by the equation below. (a) When will the missil

Question 252842: A missile is fired vertically into the air. The distance s (in feet) above the ground as a function of time t (in seconds) is given by the equation below.
(a) When will the missile hit the ground?
(b) When will the missile be 1000 feet above the ground?
h=300+500t-16t^2

I have tried several attempts at this one and nothing! Anyone willing to help, I would really appreciate it.
Found 2 solutions by stanbon, nerdybill:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A missile is fired vertically into the air. The distance s (in feet) above the ground as a function of time t (in seconds) is given by the equation below.
h(t)=300+500t-16t^2
h(t) is the height of the missile after "t" seconds.
h(0) = 300 is the height from which the missile is launched.
---
(a) When will the missile hit the ground?
When the missile hits the ground the height is zero.
Solve 300 + 500t - 16t^2 = 0
75 + 125t - 4t^2 = 0
t = [-500 +- sqrt(500^2-4*-4*300)]/-8
t = 31.85 seconds
(b) When will the missile be 1000 feet above the ground?
h(t)=300+500t-16t^2
300+500t-16t^2 = 1000
-16t2 + 500t - 700 = 0
-4t^2 + 125t - 175 = 0
Use the quadratic formula to get:
x = 29.79 seconds (on the way down)
x = 1.46 seconds (on the way up)
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Cheers,
Stan H.
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Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A missile is fired vertically into the air. The distance s (in feet) above the ground as a function of time t (in seconds) is given by the equation below.
(a) When will the missile hit the ground?
(b) When will the missile be 1000 feet above the ground?
h=300+500t-16t^2
.
Reordering:
h=300+500t-16t^2
h=-16t^2+500t+300
(a) When will the missile hit the ground?
Set h to 0 and solve for t:
h=-16t^2+500t+300
0=-16t^2+500t+300
0=-4t^2+125t+75
Applying the quadratic equation we get:
t = {-0.59, 31.84}
The negative solution doesn't make sense -- so, throw it out leaving us with:
t = 31.98 seconds
.
(b) When will the missile be 1000 feet above the ground?
set h = 1000 and solve for t:
h=-16t^2+500t+300
1000=-16t^2+500t+300
0=-16t^2+500t-700
0=-4t^2+125t-175
Applying the quadratic equation we get:
t = {1.47 secs, 29.78 secs}
The first time is on the way up
and the second time is on the way down.

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