SOLUTION: A ball is thrown downward from a window in a tall building. Its position in time t in seconds is s=16t^2 + 32t, where s is in feet. how long (to the nearest tenth) will it take the

Algebra ->  Length-and-distance -> SOLUTION: A ball is thrown downward from a window in a tall building. Its position in time t in seconds is s=16t^2 + 32t, where s is in feet. how long (to the nearest tenth) will it take the      Log On


   

Question 159118: A ball is thrown downward from a window in a tall building. Its position in time t in seconds is s=16t^2 + 32t, where s is in feet. how long (to the nearest tenth) will it take the ball to fall 175 feet?
Found 2 solutions by checkley77, stanbon:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
s=16t^2 + 32t
175=16t^2+32t
16t^2+32t-175=0
Using the quadratic equatuion:x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ We get:
t=(-32+-sqrt[32^2-4*16*-175])/2*16
t=(-32+-sqrt[1,024+11,200])/32
t=(-32+-sqrt[12,224]/32
t=(-32+-110.56)/32
t=(-32+110.56)/32
t=(78.56)/32
t=2.5 seconds.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A ball is thrown downward from a window in a tall building. Its position in time t in seconds is s=16t^2 + 32t, where s is in feet. how long (to the nearest tenth) will it take the ball to fall 175 feet?
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s(t) = -16t^2 -32t + 175
175 is the height of the building; -32 is the throw velocity downward,
the -16 is the velocity downward due to gravity.
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When the ball hits the ground s(t) = 0
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-16t^2 -32t + 175 = 0
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Using the quadratic formula, solve for "t":
t = [32 +- sqrt(32^2 - 4*-16*175)] / [-2*-16]
t = [32 +- sqrt(12224)]/[32]
t = [32 +- 110.56]/32
Positive answer:
t = 4.46 seconds
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Cheers,
Stan H.