SOLUTION: A projectile is fired vertically upward and its height s(t) in feet after t seconds is given by the function defined by s(t) = -16t^2 + 800t + 600. After how many seconds will the

Algebra ->  Probability-and-statistics -> SOLUTION: A projectile is fired vertically upward and its height s(t) in feet after t seconds is given by the function defined by s(t) = -16t^2 + 800t + 600. After how many seconds will the       Log On


   

Question 1088660: A projectile is fired vertically upward and its height s(t) in feet after t seconds is given by the function defined by s(t) = -16t^2 + 800t + 600. After how many seconds will the projectile be 5000 ft above the ground?
Found 3 solutions by MathLover1, stanbon, Alan3354:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

s%28t%29+=+-16t%5E2+%2B+800t+%2B+600
After how many seconds will the projectile be 5000ft above the ground=>s%28t%29+=5000ft
5000=+-16t%5E2+%2B+800t+%2B+600
5000%2B16t%5E2+-+800t+-600=0
16t%5E2+-+800t%2B4400=0
t%5E2+-+50t%2B275=0
t%5E2+-+50t%2B275=0

t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
t+=+%28-%28-50%29+%2B-+sqrt%28+%28-50%29%5E2-4%2A1%2A275+%29%29%2F%282%2A1%29+
t+=+%2850+%2B-+sqrt%28+2500-1100+%29%29%2F2+
t+=+%2850+%2B-+sqrt%281400+%29%29%2F2+
t+=+%2850+%2B-+sqrt%2814%2A100+%29%29%2F2+
t+=+%2850+%2B-+10sqrt%2814+%29%29%2F2+
t+=+%2825+%2B-+5sqrt%2814+%29%29+
t+=+5%285+%2B-+sqrt%2814+%29%29+
solution:
t+=+5%285+%2B+sqrt%2814+%29%29+
t+=+5%285+%2B+3.741657386773941%29+
t+=+5%288.741657386773941%29+
t+=+43.7+
the projectile be 5000 ft above the ground after approximately +43.7+ seconds

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A projectile is fired vertically upward and its height s(t) in feet after t-seconds is given by the function defined by s(t) = -16t^2 + 800t + 600. After how many seconds will the projectile be 5000 ft above the ground?
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Solve::
-16t^2+800t + 600 = 5000
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-16t^2 + 800t - 4400 = 0
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t^2 - 50t + 275 = 0
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time on the way up = 6.2917 sec or time on the way down = 43.7083 sec
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Cheers,
Stan H.
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Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
s(t) = -16t^2 + 800t + 600. After how many seconds will the projectile be 5000 ft above the ground?
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s(t) = -16t^2 + 800t + 600 = 5000
-16t^2 + 800t + 600 = 5000
Solve the quadratic for t.